The main purpose is to slow the spread, so that health care infrastructure can keep up with the demand. The quality of care also improves over time, since health practitioners learn more and more about how best to manage the disease. (In the extreme case, if we can slow the spread enough then some people will get the vaccine before getting the real virus.)

This visualizes this in graphical form.

There's a difference between "works" and "works well". I was recently scheduled to teach a 2-day short course recently; the meeting was cancelled (due to COVID19) so we switched to giving the lectures through video-conferencing and doing Q&A using a chat channel. It worked okay, but was not nearly as engaging as an in-person meeting. When courses are run well, the back-and-forth between instructor and students helps make the content more relevant and memorable. (E.g. the instructor can read body language and know when a concept needs to be re-explained.)

Overall, there are certainly lessons to be learned in terms of leveraging online education models to improve efficiency. And I'm not defending the dated "professor droning in front of bored students" teaching model, which could indeed be improved in numerous ways (including by leveraging online components). However currently there is no online experience that can replicate the advantages of in-person discussion, and thus a purely online course will not be as effective as a properly run in-person lecture+discussion.

The base-pair sequence of DNA determines its biological function. As you say, this sequence determines what kinds of proteins get made, including their exact shape (and more broadly how they behave).

But TFA is talking about the conformation (shape) of the DNA strand itself, not the protein structures that the DNA strand is used to make.

In living organisms, the long DNA molecule always forms a double-helix, irrespective of the base-pair sequence within the DNA. DNA double helices do actually twist and wrap into larger-scale structures: specifically by wrapping around histones, and then twisting into larger helices that eventually form chromosomes. There are hints that the DNA sequence itself is actually important in controlling how this twisting/packing happens (with ongoing research about how (innapropriately-named) "junk DNA" plays a crucial role). However, despite this influence between sequence and super-structure, DNA strands essentially are just forming double-helices at the lowest level: i.e. two complementary DNA strands are pairing up to make a really-long double-helix.

What TFA is talking about is a field called "DNA nanotechnology", where researchers synthesize non-natural DNA sequences. If cleverly designed, these sequences will, when they do their usual base-pairing, form a structure more complex than the traditional "really-long double-helix". The structures that are designed do not occur naturally. People have created some really complex structures, made entirely using DNA. Again, these are structures made out of DNA (not structures that DNA generates). You can see some examples by searching for "DNA origami". E.g. one of the famous structures was to create a nano-sized smiley face; others have 3D geometric shapes, nano-boxes and bottles, gear-like constructs, and all kinds of other things.

The 'trick' is to violate the assumptions of DNA base-pairing that occur in nature. In living cells, DNA sequences are created as two long complementary strands, which pair up with each other. The idea in DNA nanotechnology is to create an assortment of strands. None of the strands are perfectly complementary to each other, but 'sub-regions' of some strands are complementary to 'sub-regions' on other strands. As they start pairing-up with each other, this creates cross-connections between all the various strands. The end result (if your design is done correctly) is that the strands spontaneously form a ver well-defined 3D structure, with nanoscale precision. The advantage of this "self-assembly" is that you get billions of copies of the intended structure forming spontaneously and rapidly. Very cool stuff.

This kind of thing has been ongoing since 2006 at least. TFA erroneously implies that this most recent publication invented the field. Actually, this most recent publication is some nice work about how the design process can be made more robust (and software-automated). So, it's a fine paper, but certainly not the first demonstration of artificial 3D DNA nano-objects.

Human sorting tends to be rather ad-hoc, and this isn't necessarily a bad thing. Yes, if someone is sorting a large number of objects/papers according to a simple criterion, then they are likely to be implementing a version of some sort of formal searching algorithm... But one of the interesting things about a human sorting things is that they can, and do, leverage some of their intellect to improve the sorting. Examples:
1. Change sorting algorithm partway through, or use different algorithms on different subsets of the task. E.g. if you are sorting documents in a random order and suddenly notice a run that are all roughly in order, you'll intuitively switch to a different algorithm for that bunch. In fact, humans very often sub-divide the problem at large into stacks, and sub-sort each stack using a different algorithm, before finally combining the result. This is also relevant since sometimes you actually need to change your sorting target halfway through a sort (when you discover a new category of document/item; or when you realize that a different sorting order will ultimately be more useful for the high-level purpose you're trying to achieve; ...).
2. Pattern matching. Humans are good at discerning patterns. So we may notice that the documents are not really random, but have some inherent order (e.g. the stack is somewhat temporally ordered, but items for each given day are reversed or semi-random). We can exploit this to minimizing the sorting effort.
3. Memory. Even though humans can't juggle too many different items in their head at once, we're smart enough that we encounter an item, we can recall having seen similar items. Our visual memory also allows us to home-in on the right part of a semi-sorted stack in order to group like items.

The end result is a sort that is rather non-deterministic, but ultimately successful. It isn't necessarily optimal for the given problem space, but conversely their human intellect is allowing them to generate lots of shortcuts during the sorting problem. (By which I mean, a machine limited to paper-pushing at human speed, but implementing a single formal algorithm, would take longer to finish the sort... Of course in reality mechanized/computerized sorting is faster because each machine operation is faster than the human equivalent.)