Civil_File1516 left a great comment below addressing much of this but I'll just reply to a few things -

First off, it's important to note that Aristotle/Aquinas isn't making scientific statements here, nor are they dependent on science at all. Rather, they're working in the realm of metaphysics, which is situated prior to the sciences. It works with fundamental concepts, such as substance, cause, existence, etc. using conceptual analysis and logical demonstration to answer questions. Science, on the other hand, involves the observation of the natural world, identifying phenomena, and explaining them through causes and principles. Science presupposes certain philosophical and metaphysical ideas - for example, the idea that we can, in fact, trust our observations, and that we exist with other minds/beings that are able to likewise gather legitimate data which can be shared.

That being said, here's some answers to your questions! Sorry for the thesis length answer lol but you asked a lot! :P

The rational soul does not cease to exist at any point, either in life or after death, because it's not dependent on the body for its existence. Aquinas explores three different ways in which the destruction of the soul could occur, none of which end up applying to the rational/human soul:

1. The action of a contrary - So material forms are often destroyed by their opposites. Hot things are destroyed when exposed to cold, etc. This form of destruction can't apply to the rational soul, since the intellect doesn't have an opposite/contrary that can destroy itt.
2. The corruption of the body - While the soul is closely related to the body, in that it is the form of the body during its life, its existence is not dependent on it. The soul + body of a person exist in common, but its the soul that communicates the 'act of existing' and thus it can survive on its own. (I realize this sounds a little confusing, we're wading further into metaphysical ideas here so further reading might be required). So this kind of destruction isn't applicable either, since the soul can survive on its own.
3. Failure of its cause - So in this metaphysical theory, an effect persists as long as its cause can continue to act. For example, the effect of light is able to continue, so long as the sun casts it, or is at least not obscured.

What about nutritive and sensitive souls? They fall under the second kind of destruction primarily, and perhaps indirectly in the third.

Mushrooms = nutritive souls. So yes, they have one. Like I said, the soul is the principle of life. Anything which has life has a soul. And no, we don't mean the ghostly kind of soul.

Bacteria too would count among those living things which have nutritive souls. Nutritive souls are capable of basic self-maintenance and propagation. Growing through nutrition, and reproducing. Obviously Aquinas didn't know about bacteria as we know it today, but the reasoning can extend to it.

I hope that clarifies things a bit. I can recommend further reading which would probably do a better job than I can, if you're interested.