Do you think the Ministry would create a few measures of tracking Animaguses? If so, what kind of approaches could they take?
Hmm, perhaps they could invoke some form of The Trace on the culprit. Becoming an Animagus doesn't require a wand so I think that would make it far harder to detect. Sirius was able to turn into Padfoot in Azkaban and that magic wasn't detected, so maybe it's hard to actually detect. It's not as if you're transforming something else, you're only altering yourself.

Would that be restrictive and akin to violation of privacy?
It would be a violation of privacy, but I don't think that would stop the Ministry if the violation had been committed by a known offender. Their forms of justice (certainly under Fudge's rule) seem arbitrary.

My conjecture is that any witch or wizard , if they are willing to devote years of study, and if they are talented in both Charms and Transfiguration, can become Animaguses. What do you think?
I think you're right. Peter was able to Transfigure and he was perceived as a mediocre student- certainly McGonagall didn't rate him. Sirius and James may have been brilliant, but they were still underage.
I wonder if the studying was actually very boring and/or dangerous, so it would put off a lot of people. The Marauders and Rita had a strong motivation to become Animagi. I couldn't see Harry or Ron being that bothered by it. Hermione would be like McGonagall and want to do it because she could, though.

That's all I've got .