New V1.1 endpoints question



Suppose, my screen name is @myscreen

Can anyone answer which API (endpoint) should I use for:
Q1. Finding : is @screen2 a follower of @screen1?
Q2. Get : numbers of followers of @screen1
Q3. Get : numbers of people @screen1 follows
Q4. Finding : Is @screen1 timeline private or public ?
Q5. Finding : Has @screen1 twitted a specific message “abc xyz #klm” in last [x] minutes?
Q6. From Q1 to Q4, Can I make 3,000 calls an hour for different screen names for those endpoints?
a) if not then what is the rate limit
b) if 3,000 exceeds rate limit, then what is the solution?