1. Most infantry can sap. Yes pike units can. Just right click a selected unit on the sap point and they'll start digging.
Sap points can be destroyed by enemy fire.

2. Running units onto the battlements above the gate will enable them to capture it eventually. Running units through towers does the same thing.

3. That extra level is for large stone walls and above. The siege towers shoot back from that floor automatically. You cant put guys up there tho.

4. Usually rams/siege weapons take priority, and the castle defences will always target siege weapons. A stone wall gatehouse will always take out a ram by itself.