That depends on the book. In Socerers Stone, they go to the tower to help release Norbert, the illegal baby dragon Hagrid won in a pub
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To meet Charlie's friends to take Norbert away
No, because Harry and Hermione were back in time as the real Harry and Hermione were living through it. Hermione throughs a stone at Harry to get him to notice the executers.
No, Emma Watson is not going out with Tom Felton. They are just good friends.
They kissed in the 7th movie/book, Harry Potter and the Deathly Hallows, but they did not officially "go out". At the end of the book, in the Epilogue, Ron and Hermione are married with 2 kids, Rowling never said anything about them dating though.
Ron Weasley and Hermione Granger do fall in love, this is confirmed in the epilogue of Harry Potter and the Deathly Hallows, where Ron and Hermione are married and meet Harry and Ginny (who are also married). Ron and Hermione are saying goodbye to their children, Rose and Hugo Weasley. Ron and Hermione have liked each other for a long time. For example, Hermione was upset and jealous when Lavender Brown (played by Jessie Cave) and Ron where seeing each other in Harry Potter and the Half-Blood Prince. This also happened in Harry Potter and the Goblet of Fire, where Hermione and Viktor Krum are seeing each other and go to the Yule Ball together. Ron was jealous this time.
Harry Potter and the Deathly Hallows Part 1 isn't set at Hogwarts and Professor McGonagall was still teaching there. She appears in the second half of the movie when Harry, Ron and Hermione go back to Hogwarts.