This is from what I've read, if it is incorrect hopefully someone will correct me.

Question 1:
Typical quoted sustained fire rates for well trained, full crews of light artillery in the ACW is around 2 rounds per minute per piece. That is what was expected. The frequency could be accelerated considerably when under pressure. For instance, against infantry at close range canister would be used and no real aiming would be needed (a time consuming step.) Sponging the barrel could be skipped for several rounds (at risk to the loader.)

A 3" rifle carried 50 rounds per ammunition chest. Each piece would have 4 ammunition chests assigned to it, one on each limber, two on the caisson.

I would expect a steady continuous bombardment to be maybe 1 round per minute or slower assuming there was no sense of urgency and accuracy was considered more important, but that is just a guess on my part. There would be no reason to fatigue the crews as long as they were not receiving counter fire.

Larger artillery such as siege/seacoast guns and large naval cannon took considerably longer to load and fire--something like 2 minutes per round for sustained naval firing is what I've seen quoted.

Question 2:
The limber is for moving the gun and other "accessories." The limber is a two wheel carriage consisting of the front axle and draught pole set that is harnessed to the horse team. A gun or caisson was connected to the limber so that the limber could tow them (the gun or caisson would form the rear axle set.)

The limber was designed to have a single ammunition chest mounted on it which also served as seat while being driven.

The caisson was the main ammo wagon for the piece, plus it carried a few spare parts a wheel, and tools. It carried two ammuntion chests. So each gun had its own limber, and its own caisson with limber. The caisson could go back to the supply wagons and replenish ammunition chests while the piece remained in action (assuming that the wagons weren't far in the rear or were not inaccessible due to terrain, enemy units, etc.)