1. I think Neil would have had the idea of committing suicide but not actually doing it if Mr. Keating never came into his life. Reason why is Mr. Keating told Neil that he should be doing what he loves instead of what his father wants. He wanted Neil to actually be himself not what his dad wanted him to be or do.
2. Again I think Neil was the bravest of the Keating boys. He actually took what Mr. Keating had said and did what he loved even though his father didn't let him. The coward of the Keating boys was Cameron because while everything was happening he didn't really do anything he wanted and when things went bad he was the one to tell on everybody.
3. Mr. Keating gave Neil the book because he knew Neil was going through a tough time and Keating thought it would help.