It's a matter of denotative vs. connotative definitions. Free will proponents are saying, "hey that thing we all do when we make a choice that rocks can't do, that's free will", and you're saying "free will has such and such properties, so whether we have it depends on whether our choices have these properties".
I'd argue that most people reason denotatively, in which case merely pointing out the thing we're trying to define suffices as an existence proof. What remains is defining what it is, logically.
> 1. Determinism or not, free will doesn't exist in either case
It sure does!
> The whole idea of "me" being a singular, well defined thing is purely an artefact of human language. We are a process, not a thing.
Agreed. I don't see why this poses any difficulty. The behaviour of the process is largely governed by free will, just like a process on your computer will often sort lists.
> If free will is so real, can you freely choose never to choose again? Of course not.
Sure, via suicide.