Are my pronouns he/him?

Probably. Your pronouns are what you want them to be. If someone says "I saw shapis at the park yesterday, but he looked busy so I didn't say hi to him," are he and him what you want in those positions?

(I'm going to assume you're a he/him for the rest of this, but if you want something else let me know and I'll edit the post.)

Is that how I should tell people?

Yeah, you'd say "my pronouns are he/him."

Do you actually tell them as you meet them? Do I have to wait for a certain social cue?

In person, it comes up in group meetings where people are making an effort to be inclusive, typically gender diverse or far left crowds. Someone will mention it, or people will just start doing it. You don't have to be the first person to start adding pronouns. But if you're in a crowd with someone you know would appreciate it, it'd be nice to start it on your own (without singling them out).

The most awkward option is that you introduce yourself without pronouns, then it goes around the room and people start; in that case just pipe up and say yours are he/him.

How about online. Should I tell people or have it on my personal profile somewhere?

Having it in your profile online is a good idea. Online it's way more important, since it also combats "there are no girls on the internet."

And about respecting other people's pronouns. How do i figure them out? Is it a big faux pas if I don't before I know them? Is it a faux pas if I refer to someone I just met and I assumed to be male as he/him?

If someone has a gender presentation you can't figure out, ask. If you're pretty sure, guess. It's a minor faux pas to get it wrong, but it's within the realm of the inevitable awkwardness of human interaction, just say sorry once, correct yourself, and move on. Think of it as being as rude as accidentally stepping on someone's foot. (Think about how rude that'd be if you kept doing it though.)

I've never seen anyone referring to anyone irl by non conventional pronouns. Is it an actual thing or is it currently being pushed to make the world a more inclusive place?

It is very rare, but they're out there. People with really unconventional pronouns (I've met a fae/faer) are going to understand if you have to slow down when talking about them. Generally they're chosen by people whose gender identity is nonconventional enough that they're willing to put up with the hassle to get something that feels more right to them.