> Which is to say, if you say you're a "trans woman", am I able to infer that your desired gender pronoun is female?

Yes, this is indeed a generally safe assumption. View "trans" like any other self-descriptive adjective. "I'm a tall woman", vs "I'm a trans woman". It's not an absolute given, because nothing is black and white (some might prefer gender neutral pronouns), but generally safe.

The best way to know for sure is to ask them instead of making any assumptions.

Truly we have transcended parody.

I'm not trans but have several trans friends, and just wanted to add (as a non-trans person), make a best guess for how someone presents and if they correct you, do not joke about it. No jokes, no extra comments, Just say, "sorry, got it," and move on. It's a matter of respect and nothing more, and if you respect someone, it's easy to show it. Making a joke about something that's important (and possibly sensitive) to someone is just a bad start.

I don't think it's necessary to be so careful. If they can't take a joke I don't wanna hang out with them.

You would use she/her pronouns for trans women, and he/him pronouns for trans men. Just treat trans women as you would any other woman, and trans men as you would any other man.

Generally people who prefer neutral pronouns will identify as nonbinary, genderqueer, or perhaps transmasculine or transfeminine, (although not all people who so identify prefer neutral pronouns) and you might need to ask them for their preference.