Can my boyfriend sponsor me even if he had a previous sponsorship with his ex-wife?

Generally, a U.S. citizen who marries a foreign national who entered the U.S. lawfully and with inspection (such as with an F1 visa), may sponsor the spouse to adjust status to become a Lawful Permanent Resident (to get a "Green Card"). This is true regardless of whether the U.S. citizen may have sponsored a former spouse whom he later divorced. Under these circumstances, the application process can be more complex than with ordinary cases, and it may be necessary to provide documentable evidence that both the first marriage was bona fide notwithstanding that it ended in divorce, in addition to providing documentable evidence that the newly married couple is living together in a bona fide marriage. Appropriate documentation for each of these requirements is determined by the USCIS on a case-by-case basis, but generally includes such things as documents showing the couple live at the same address (a lease or house deed), showing the couple have put their financial lives together (joint bank account statements showing each spouse placed his/her earnings into the account and household expenses were paid from the account), showing that one or both spouses are listed on utility bills, showing car and insurance registration, etc., etc. There really is no substitute for you and your fiance to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options, and strategies to attain your goals, and who then could offer legal representation in the often complex application process.

You're asking a few different things, and for a few different forms of relief. I'd have to get more information about your boyfriend, and his past relationship.