1) Can other troops besides the one that manned the siege towers and ladders use these tools after the first troops break through?
YES. You can assign units to "go up the wall" and they will find the route through the siege towers and ladders.

2) Does it make a difference if you use archers to push a siege tower? Hence can they shoot from it?
Archers can't shoot when they are walking (in the siege tower). Siege tower comes with its own arrow towers, but can only function if the pushing unit does not have missles (that excludes all nicer Roman infantry, unfortunately).

3) I had reinforcement come in and they were right where I positioned my troops, however, since that they were behind the red line and AI controlled (I think), they never moved??
Besides the AI controled general issue, this might be because your 20-max unit limit is reached, so they can't enter the battlefield yet. This also happens in non-siege situations. (btw, without reinforcement, your opponent has mostly 20 units of cavalry, too.)

4)When receiving reinforcements, can you control them by not assigning a general to that group?
YES. Actually you should always do that unless you want to experience one of the 7 "RTW player's rages".