I am a researcher working in hydrogen & fuel cells, so I'll just spill the beans:
And the hydrogen probably takes up more space than a gallon of gas (a guess --- does someone know?).
It does, but not so much. Storing H2 at 700 bar requires a hefty pressure tank. They are fairly safe but that doesn't make them lighter. That's why hydrogen is suited for larger vehicles (family wagon, SUVs, long-range trips, trucks etc.). Short range is better served by batteries.
What are we destroying to make the hydrogen?
If you have cheap electricity, then it's water. You electrolyse it at the station and do not need to ship hydrogen around or build a gas network. You can also reform natural gas, which is cheaper, but then you need to clean the hydrogen really well: requirements on purity are 99.99% hydrogen, and other components are very severely limited (e.g. sulphur down to 4 parts per billion). It is debatable whether the purity standard is really necessary, though, it may be unnecessarily strict.
Main reason not to use electricity directly, as in batteries: batteries are heavier, and if you want to double energy storage in a battery car you need to double the batteries (which is not going to double the range—the batteries are heavy too). If you want to double the energy storage in a hydrogen car, you only need to double the hydrogen storage, the fuel cell (the expensive part) is still the same. And hydrogen storage is not nearly as heavy as its battery equivalent, also factoring in that fuel-cell conversion is about 50% efficient.
Why is investing in a new infrastructure -- hydrogen distribution --- a good thing?
As I said above, a good alternative is not to have the infrastructure, but to produce and compress hydrogen locally at the station. The idea is that even with all the losses (hydrogen production, compression, fuel cell) the system is still more efficient that oil (drilling, extraction, transport, refining to gasoline, transport, combustion engine). More importantly, hydrogen can be produced starting from anything: natural gas, oil, solar, you name it. Gasoline comes only from oil (or coal if you want to go Fischer-Tropsch, but that's not really efficient and has large emissions).
Does this process change the net amount of water in the ecosystem in a way that would have impact in 50 years?
No, the quantities are minimal compared to the oceans. Any day you will have far more water passing through your shower than out of your exhaust. 100 km of travel in a fuel-cell Mercedes B-class (yes I drove it :-) produce about 9 kg (i.e. 9 liters) of water. Besides, that hydrogen was produced from water from the biosphere anyway, so no balance is disrupted.