1. I believe the CBA expires June 30, as the new league year begins on July 1. However, nothing would stop the owners from "locking out" the players before that, like the NFL did.
2. Teams can complete trades once they're eliminated from the playoffs, but they can't trade players whose contracts are expiring or which could expire due to options.
3. The draft is June 23. It will most likely go forward, although players are likely to be signed under whatever new rules are agreed to.