After admission, should I thank a recommender who I suspect wrote a bad letter?

Yes, you should thank and inform your letter writer, and no, you shouldn't worry about some bizarre and unrealistic "re-evaluation" of your admission.

Comments: It is very unlikely that your writer wrote a negative letter. In general, one only agrees to write a letter if one has something constructive or positive to say. Having read lots of letters, I'll note that even judgmental and perfectionist people put their criticisms in context, comparing to their general assessments of other students or researchers. (I.e. this person isn't perfect, but he/she is better than most others for the following reasons). These letters, in fact, are often the most compelling.

As a further comment, you're being very uncharitable in assuming bad intentions of someone who agreed to write a letter for you!

And a final comment: no university is going to care to "re-evaluate" their admission of you, even in the stunningly unlikely event that someone asks them to, except in cases of actual fraud, criminal issues, etc. Everyone involved has better things to be doing with their time.

The fears you describe go way beyond your characterization of this person as perfectionist/judgmental into extreme pettiness. To go to those lengths would be to put a lot of effort into sabotage. If I were the committee/professors at your new institution on the receiving end of comments like those, especially from someone who I knew previously wrote a recommendation letter for the student, I would lose respect for that professor and their opinions, not for the student, and I would wonder why they are spending so much effort to bad-mouth a student at my own institution.

I think you have little to lose by a polite thank you and informing that you will be attending University X, unless you have other reasons beyond this professor's perfectionist/judgmental tendencies. You probably won't need their recommendation in the future, so no need to worry about that.

Yes.

If he wrote you a good or even half-hearted recommendation, a sincere thank-you is common courtesy, and will cement his good opinion of you (it's even possible he wrote you a glowing recommendation -- your biggest boosters sometimes come from surprising places).

If he wrote a neutral or bad recommendation, he's more likely to remember your graceful response and think better of you (and it's still basic courtesy).

If he despises you, wrote you a strongly negative recommendation, and you got the job anyway, a polite and sincere thank-you will be the most galling retort you can send.