Summer holiday puzzles

With the end of the school/coaching year, here are a few puzzles to keep you thinking for the next few days at least.

1. Place 8 queens on the board so that none attack any other queen (OK this is a well known puzzle)
2. How many queens can you place on the board so that all squares are attacked? (Queens are allowed to attack each other in this case)
3. Place a bishop on a1 and pawns on every black square. Can you move the bishop to h8, capturing a pawn on every move? (This is equivalent to a Bishops tour where every square of the bishops colour is visited while playing distinct moves. Visited squares can be crossed, but not stopped on)
4. Is it possible the cover a 5x6 board with dominoes in such away there are no straight edges that extend across the board? What about a 6x6 board?
5. Place pawns on e8, e7, e6 and e5. Is it possible to divide the board into equal continuous areas of 16 squares each, so that each area contains a single pawn?

(Some of these puzzles were courtesy of my fellow coaches IM Andrew Brown and I.M. Hosking, while others were sourced from "The Mathematics of Chessboard Problems")