Stating the Obvious

With regard to your first example, the fallacy you’re suggesting is Equivocation; where a term is used in an argument more than once with different meanings of the term in each use.  But I don’t think B is committing  the Equivocation fallacy or any other fallacy.   

Rather, B is pointing out that the desire for everyone to have access to free health care needs to be weighed against the fact that someone has to pay for it.   If people are ok with higher taxes, then the government can give more services.   Regardless of whether one agrees with A’s comment that it would be a good thing for all Americans to have access to free health care, B’s point is neither fallacious or trivial.  

Yes, the second example struck me as being a strawman too. It's just silly. Those who argue for renewables are perfectly conscious of the fact that solar panels don't work at night (or even in certain weather) and recognise that fossil fuels will be depended upon for a regular supply of energy until renewables are up to the task.

I'd like to dig into that second one a little more. It's factually incorrect to say that it's impossible for a home that uses solar energy to run appliances at night, but there are some (at least seemingly) plausible scenarios where they wouldn't be able to. The core of the argument of someone taking B's position may overly focus on the fact that solar panels only generate electricity when the sun is out, while ignoring the fact that battery backups and secondary power sources exist to resolve this issue. Maybe if this argument was phrased another way:

"These politicians say we should be using solar energy. Well, I have news for them, the sun doesn't shine at night!"

The factually incorrect statement is removed, but the argument is still basically the same. After writing it out, I'm inclined to think this might fall under cherry picking .

And, to be charitable to B's position, there is one scenario where this criticism is at least somewhat valid. That is that homes with grid-connected solar aren't typically equipped with battery backup, so in the event of a nighttime power outage, they'd be no better off than someone with no backup power at all, but worse off than someone who owned a fuel-powered generator. That is, provided that fuel is available, which isn't guaranteed during a widespread blackout.

I think to call this statement a fallacy may be overreaching. It is really just rhetoric, that even as it is written, is based on a misunderstanding of solar power. Politicians aren't talking about solar setups for each home; they do talk about adding more solar to the grid. In virtually all situations grid-related,  the sun going down isn't a problem.

Both examples seem like rhetoric and opinions to me; not much developed argument is going on.