From my (not a chemist) reading of the paper:
If you have a battery which is consuming sodium to produce electricity, you want the electrolyte around the cathode to be acidic, and the reaction will be producing OH-, neutralizing acids. Continuously dissolving CO2 into this water produces a source of acidity, so the CO2 not only makes the battery works better, but it simultaneously sequesters the CO2 as NaHCO3.

I think this really is the core of the proposal - make the battery work better and sequester CO2 at the same time.

Your suggestion of throwing Na into water wastes lots of energy - it has the same H2 production as the Na+CO2 scheme, but doesn't produce any electricity.

Yes, you need to use electricity (more than you get out) to create metallic Na, so this is a battery rather than energy source, and TFA deceptively omits this. I don't know how efficient this battery would be.

From my skimming of the paper, they'd be getting replacement sodium from sea water, not from the sodium bicarbonate which they produce. That would be sequestered somewhere.

Reading a bit more (I am not a chemist):
"Because the potential of cathodic reaction is closely influenced by the pH of aqueous solution, the dissolution of CO2 renders a favorable electrochemical reaction environmentby acidifying the aqueous solution."

"Thus, notably, this combined cathodicreaction not only utilizes CO2 to generate H2 but also possesses highly efficient reaction kinetics,possibly overcoming the key issue of sluggish discharge rates for common metal-air batteries."

Figure 4 shows this is a rechargeable battery!
"On repeating the discharge-charge process, the cathode potential profile(Ecathode) presents discharging and charging plateau, clearly proving that this system is rechargeable."

"To confirm the reversibility of hybrid Na-CO2cell, the anodic charge profile (electrolysis profile) was observed. Because Na is one of the most abundant elements on earth, Na metal anode could be easily recycled through a charging process in Na-ion-containing aqueous solution, such as seawater. Figure 4A shows an oxidation rotating disk electrode profile for examining whether CO2 was reproduced during the charging process. Generally, the charging process is regarded as the opposite reaction of the discharging reaction. In this work, however, the generated H2 gas from the discharging process is naturally removed on the surface of electrode, and thus the oxidation reaction proceeds as the oxygen evolution reaction (OER) from the water oxidation (Equation 6).
2H2O -> O2(g) + 4H+ + 4e- Eo= 1.229 V"

As this equation does not involve Na, I'm still unclear on how they are regenerating their Na.

Help! Is there a chemist in the house?

The paper can be downloaded (no paywall) from here. Equation 5 "Net equation" is
2Na + 2H+ -> 2Na+ + H2, E0 = 2.71V.

So yes, it works by consuming sodium metal. I am underwhelmed.

How much energy could we get from the metallic sodium if we didn't turn CO2 into NaHCO3 as a side reaction? What is our efficiency at making metallic Na? If these cells are sufficiently cheap, reliable, high power output, and efficient there might be potential for using this for grid scale energy storage in the form of metallic Na. Doing so would have an advantage of energy storage being limited only by your ability to store sodium, so it could work on seasonal timescales. Of course, then you'd have seasonal H2 production which would carry its own storage issues.

The TFA starts:

This immediately primes a bunch of people to look for fault with the rules, and another bunch of people to ignore any possible faults with the rules. Why not say "The FAA on Monday ..."?

Is this something driven by political office holders/appointees, or is it just the FAA doing its job and modernizing its rules as best it can? Technically anything federal government does can be attributed to the Trump administration, but it is misleading to make this attribution unless the action was directed by someone at the Whitehouse.

The TFA does say

This is some justification for bringing the administration into it, but without more information I'm left wondering how much influence this program had on the proposed rules. Does anyone have information to show a connection?

This really is a return to its roots for advance fee scams. A famous 19th century version of the scam was the Spanish prisoner. A wealthy person is imprisoned, needs a little bit of cash to escape, and will reward you afterwards.

Where is its safe initial aim point when doing a return to launch site (RLS) on the west coast? Is the landing site close enough to the coast for this also to be at sea?

The west coast launch a couple of days ago could have done RLS, but was not allowed to because another rocket was readying for launch on another pad, and they didn't want an unexpected booster falling on them. I expect (justified or not) this event will reinforce that worry.

Paternal leakage would almost always cause heteroplasmy (unless the father happened to have the same mitochondrial genome as the mother.) Sequencing can indeed detect biparental inheritance.

If an individual was heteroplasmic due to paternal leakage when they were conceived, and the individual was female, she could pass this heteroplasmy to her children. There is a 'bottleneck' in mitochondrial genome number per cell, and if those genomes are randomly chosen from the mother's heterplasmic selection, the proportion of the two alleles will randomly shift. The smaller the bottleneck, the greater this random change will be.

I'm a coauthor on some papers looking at mitochondrial heteroplasmy where I was doing the maths to figure out the size of this bottleneck. (In penguins, about 30, in salmon, about 100 - but uncertainty was quite large, I think about 30%.) As I recall, different organisms can have quite different bottleneck sizes, and I think human bottleneck is quite small. (I haven't looked this up, so don't rely on it.) This means it would likely be only a few generations before the heteroplasmy resolved itself (one of the alleles would 'fix')

Modern sequencing techniques could not only very accurately measure the heteroplasmy proportions, it could also detect whether some sequences had undergone recombination, as it can give separate reads of thousands of individual DNA strands. The data I was working with used older 'Sanger' sequencing and could only give approximate averages over many strands.

Only to a limited extent. It depends on how often this happens, and whether mitochondrial recombination is a thing.

"Normal" (nuclear) DNA undergoes recombination: there are two (not quite identical) copies of the genome, and bits get swapped between the copies, so a chromosome you got from your mum has bits that came from both of your maternal grandparents.

It is hard to know whether this process also happens in mitochondria, because the mitochondrial genomes seldom differ, and when they do, it is very likely they do so at only one place. If there is no mitochondrial recombination, then all mitochondrial genomes are inherited strictly from one parent, one grandparent, one great-grandparent etc. Mitochondrial Eve holds up fine, it is just that now those mitochondrial lineages very rarely are inherited through a male. The ancestry is still strictly a tree, where a 'parent' may have multiple 'children', but a 'child' has only on 'parent'. ('Child' and 'parent' here are individual mitochondrial genomes.)

I know there is research into mitochondrial recombination, but I don't know the field well enough to comment on the conclusions of this research.

Once you have recombination, the tree breaks down, and two mitochondrial lineages can merge together into a hybrid. However, if this is very rare (as seems to be the case) then the tree rooted at Mitochondrial Eve is still a very good approximation. In particular, it is still very likely that the entire sequences of all modern human mitochondria are descended from the mitochondria of a single woman.

I came here to point out that the summary is rather overstating the case, but your link does a much better job of it than I could.

The concept of paternal inheritance of mitochondria is sufficiently known to science that it has a term to describe it: "paternal leakage". It is something which has been observed in a number of organisms, although I think it is always rare. (As I recall, interspecies hybrids are more prone to paternal leakage, so sometimes what you observe in the lab may not be happening in nature.)

I'm at home, so I don't have institutional access to read the paper, but from the abstract and the blog post above, it looks like an exciting result - just not as exciting as the media reporting makes out. This is like finding a species suspected to have been extinct for a few decades, rather than being like finding the Loch Ness Monster.

If Blue Origin develop New Glenn into a heavy variant (three cores) and if BFR doesn't happen as planned, they'll be the only cheap option for getting very heavy payloads into space, and can make a profit if lots of people decide they want to take advantage of this by designing very heavy payloads. There were a whole lot of 'if's in there.

FH has similar capabilities to NG, is already flying, has hardware proven by 60 launches, and has construction facilities optimized during the building of >60 rockets. Both rockets expend their second stage, but FH's second stage is smaller, so I expect is cheaper.

Few current payloads require the capability of FH or NG. Where SpaceX can offer F9 for smaller payloads, NG is all or nothing. Even if both rockets were equally mature in manufacturing and launch experience, I think the F9/FH combo would be more economic than NG.

If NG turns out cheaper than FH and the market reacts by building many payloads requiring NG or FH, then NG may turn out OK in the long term - but nobody would have been committing serious money to building such payloads prior to FH's test launch, so they are years away still.

Blue Origins huge advantage is they have very deep pockets behind them. If NG flies, recovering R&D costs is optional. Unless Musk cashes out of Tesla, SpaceX has to pay for R&D as they go.

When I was near finishing my PhD, I had my most recent backup close to hand, an older backup in another building, and a still older (but only a month or so) backup in a different city. I wasn't going to lose my thesis to no house fire or meteor strike.

There are many companies hoping to compete in this market. Starting from this wikipedia page, I find

(rocket, company, country, first or planned first launch date, payload to low Earth orbit)
Operational:
Kuaizhou 1A, ExPace, China, 2017, 300kg
Electron, Rocket Lab, New Zealand and USA, 2018, 225kg
Zhuque-1, Landspace Technology, China, 2018, 300kg

In development:
OS-M2, OneSpace, China, 2018, 205kg
Vector-R, Vector Launch, USA, 2018, 60kg
Vector-H, Vector Launch, USA, 2019, 160kg
SSLV, ISRO, India, 2019, 500kg
Bloostar, Zero 2 Infinity, Spain, 2019, 140kg
Hyperbola-1, i-Space, China, 2019, 300kg
Arion 2, PLD Space, Spain, 2021, 150kg

I think there are a few more too. Payloads are not necessarily to the same orbit, so are only an approximate comparison of capability. I haven't fact checked this list. Future launch dates are of course speculative.

New Zealand innovation, California money.

According to Wikipedia: Founded 2006 in New Zealand by a New Zealander, and funded by another New Zealander. They launched a sounding rocket in 2009, proving their rocket design. First outside funding mentioned was in 2013. (I take no responsibility for Wikipedia's potted history being complete or accurate.)

I'm sure that once the money came along, so did extra expertise, so it isn't 100% New Zealand innovation, but that is where the big steps were taken.