[Radek]

The air problem:
1. The Athletics skill increases the time you can spend under water considerably. With Athletics 12, you can afford to do Collasium without underwater breathers (using Breath of Air and Restore Health spells).
2. The Iron Lung trait doubles the time you can spend under water. There are 2 sources of the trait:
a) You can buy the trait in the thieves guild when you reach level 5 for the guild. I am not sure whether everybody is offered the trait or whether only thief-like roles are offered it.
b) The Ring of Neptune (Collasium) contains the trait. The ring is in the 4 stars chest near the exit from Collasium.
With the trait and the skill, you can forget underwater breathers completely.
3. The Breatch of Air spell (Vine magic, level 6) clears the "drowning bar" completely. But it also takes one half of HP of the caster away. Use the spell with the Restore Health spell (Spirit Magic, level 6) - and only if your Athletics is enough high. Otherwise, you will be so busy with casting the spells that you will be unable to do anything else.
Summary: the primary tools are the Athletics skill and the Breath of Air and Restore Health spells. Later on, you can gain the Iron Lung trait.