1. I hate to see it change.
— I would call "change" an infinitive, in that example.
2. As you might imagine, this did not make the judges the happiest people I’ve ever seen.
— "might" is a modal verb: it expresses a possible "imagining" of the addressee, at the moment of speaking.
"Did not make" is a past tense: the event described occurred in the past.
"I've ever seen" is a present perfect: it expresses a continuum of "seeing happy people" in the speaker's lifetime, up to the moment of speaking.
All the best,