Not unless that lane is specifically marked or signalled as such. Normally you may only turn right on red from the lane closest to the right curb.
Yes, it is perfectly legal.
Before this can be answered you need to clarify which lane you think is the "inner" lane.
yes
Usually, no. It is legal ONLY if the turn is specifically authorized by signage at that location. If that information is not posted, a turn from the cernter lane is illegal.
Unless the lane is specifically marked as "Right turn permitted without stopping", yes. In any case you would still be required to yield.
Wait for the traffic light to turn green the proceed carefully...
This means you cannot turn. If you are in a turning lane and you see a red arrow you must wait till it is green before advancing.
Yes, they do. If you have a green signal to turn left, the opposing lane will have a red light. Even though vehicles may turn right on red (unless otherwise indicated), they are still required to stop and yield right of way on a red light.
Yes I think
Only from specifically marked lanes where it says so. But it is not allowed in most of NY.
You can turn right on a red light and a left red arrow. If there is a sign that says "no right turn on red" or it's a right red arrow, you can't turn right.