Need info on submarine's pump, compressor etc.

[EFileTahi-A]

First of all, I apologize if these are stupid questions. My knowledge in submarines is not that great, specially regarding modern models.

These are the questions I would love to have them answered:

1 - What is the purpose of a the submarine's pump?
2 - What is the purpose of the compressor?
3 - By having larger ballast tanks will this increase the subs ascending / descending speeds without using the engine?
4 - By having larger ballast tanks will this increase the flood capacity of the ship? That is, will the submarine be allowed to have more compartments flooded before beginning to sink?
5 - Imagine 2 submarines engaging each other. Will the depth factor influence anything? I mean, by going deeper will any of them gain the upper-hand in the duel?
6 - Can high water pressures be used as any source of energy at all?
7 - Will the sonar and torpedoes be influenced by extremely high water pressures?

Thank you for any possible info on this matter.