Its unlikely that existing data sets contain the info you are looking for. The US Department of Education’s National Center on Education Statistics produces a number of large surveys of high schoolers moving on to college or first year college students followed over time, but these are unlikely to contain the information you are seeking.
For some topics, it is possible to do research on twins at the Annual Twins Festival in Twinsburg Ohio:
I think it would be more likely identicals would go together and fraternals would be like any other siblings. My d was friends with identicals. They are a package deal. Both girls are at the same school now, but not roomies. They clearly still just hang out only with each other. One of them desperately needed to get away from the more domineering one, but that didn’t happen.
My son has twin friends at MIT. I think college admissions does find it a novelty, but I have no proof it’s an edge in admissions.
Here’s more anecdotal information in response to your first and second questions. Of the sets of twins I’ve known well:
Identical girls: Went to same very selective public university and roomed together. For both, it was their dream school, financially affordable, and they both were highly qualified. They had roomed together growing up and didn’t want potential roommate problems with other people.
Identical boys: Went to same public university and roomed together. Both received academic scholarships.
Identical girls: One went to an LAC, the other to a community college. They are very close and wanted to go to the same college. However, one was considerably brighter than the other, plus they had different interests. They ended up only 20-30 miles apart and spent a lot of time together.
Identical boys: One went to a very selective private university, the other to a less-selective public university probably around 200 miles away. Again, different interests and different achievement levels. They are also quite comfortable with not seeing each other for months at a time.
Identical girls: Went to the same LAC, roomed together, and have lived together since. They were the “always wore the same outfit, always did the same thing” type, so they weren’t going to be parted.
Fraternal girl/boy: Girl went to public university and boy went to a different public university, then transferred to a private university. I don’t think they tried at all to be in the same place. It made it difficult when their graduations were on the same morning. Their mother went to one and their father to the other.
There is lore that some schools (including Yale) “like” to take both twins. It may just be that identical twins tend to have resumes that are similar enough that it makes sense to take both or reject both.