Board Game Arena

It's not clear at all to me what make me an offer does in the trade window and it's not explained anywhere. If I say I'll give some things, and ask them to make me an offer, do I just give them stuff for whatever they decide to give me?

If they make a counteroffer, you have to agree on that first. It's not automatically accepted if they make a counteroffer to your offer, otherwise it could be abused.

It could perhaps use a help button to explain, though it does indicate in the summary that they well send a counter offer. And no, you don't have to accept.

The main uses are to show someone a promissory or action card secretly and ask the other player what they will give you for it.

And, if the other player said they had a good secret card, this is a way you can request it. There is no way to just request "You give me your Sabotage" because you technically don't know they have it, and it would be bad if "go fish" type trade requests started showing up for action cards.