Addressing your points in order:
1. I've had to address this a lot, which does show that I made it unclear in the writing, but it's a bit late for that at this point. The obligation Taylor was referring to was a social obligation, not a legal one. Basically, she's worried about two things: looking weird in the eyes of the public by leaving the Protectorate after going through the Wards—which is mostly just social anxiety, people wouldn't actually care about that—and sending a signal to villains that there's now a Tinker without their old teammates. Joining the Wards puts you in the public eye, and then leaving the Protectorate says "and now I'm vulnerable." In that way, she's obligated by the nature of the Wards and the Protectorate to join through to the Protectorate when she's done in the Wards, or else run a gamut of problems.
2. There's also nothing in canon that contradicts Tinker and Thinkers being abducted, and it makes sense for them to be. They have powers which can often be incredibly useful support powers, tend not to be well-suited for self-defense, and can all become
massive threats if allowed to accumulate resources.
3. I missed that, but don't so much mind: I've made bigger changes to the canon for this fic already.
4. See above.