The most basic use of these words is as demonstrative pronouns, that much I've figured out

Examples:

This is a car.

Why don't you pick that up.

One thing I'm unclear on however, is their function in sentences like these:

What is that thing?

These papers are in my way.

It seems in these sentences, "that" and "these" function more like adjectives than pronouns. I.e. Which thing? that thing. Which papers? These papers.

So what are these damn things called when they're used that way? Or are they still considered pronouns?

I think that they are called "determiners" in those cases.

That is correct. It's called a demonstrative determiner.

Thanks.

There you are then, as they say.Who are these theY though?

Demonstrative adjectives is the technical term, I think.