Minvera McGongall was the acting headmistress during the final battle but she had retired by the time Harry Potter's children were at the school. It remains unknown who became the headmaster after...
No, in Harry Potter and the Deathly Hallows Snape is elected Headmaster of Hogwarts, and Professor Slughorn is reinstated as Head of Slytherin.
Fourteen years, as of Harry Potter and the Order of the Phoenix. In other words, since the year Voldemort was defeated by baby Harry.
Gryffindor.
No, Voldemort killed Snape.