1. false (M.V. Lomonosov)
2. false (in was founded in 1755)
3. true (only peasants (крестьяне) were unable to study there)
4. true
5. true
6. false (I worked at selection committee this year, you can do it either by post or yourself)
7. have no idea, what NSE means there.
8. true
9. true
10. true
11. true (1756 - MSU, 1776 - Bolishoi - wiki information)