I say the odds are good.
MOP qualification means that the OP is among the top few dozen math kids in the country. If the teacher recommendations are positive, with a particular emphasis on “nice”, and you couple that with good essays, chances of admit are high.
I know a number of kids that made USAMO but didn’t make MOP. Almost all of them were accepted to MIT, and the one that didn’t “settled” for CalTech.
Not really. There are typically no more than 30 kids graduating each year who ever made it to MOP, and not all of them choose MIT as their first choice. Some will choose places like Harvard, Stanford, or Princeton and get in early, so MIT never sees their applications. Perhaps 15 kids at this level show up on MIT’s radar each year.
And this doesn’t even begin to look at the other qualifications, which I know less about.