1. No, not for bouldering, though it helps to have climbing shoes.
2. It's generally considered impolite to give advice on how to climb something, unless the person asks.
3. Most bouldering/climbing gyms have small workout areas in addition to the walls, and memberships that aren't a lot more expensive than a regular gym.
You can just show up any time the gym is open. There are bouldering walls, just find a problem (what bouldering "routes" are called) that no one is on and go for it. Gym bouldering is usually pretty social, most people will be happy to answer any questions you have about anything, easier problems to try or techniques, etc.