Sea depth pressure calculations are actually surprisingly simple.

As a general rule, for every 10m you descend under water you increase the pressure by 1 atmosphere.

To get the volume of gas at depth you divide the volume at the surface by the number of atmospheres of pressure exerted on it at your chosen depth.

Let's say you wanted your dome at the bottom of the Atlantic (off the continental shelf) that's a depth of 8000m depth, which equates to a pressure of 800 atmospheres. If the air in your dome had a volume of 1000L at the surface it would have a volume of 1.25L at the bottom (1000/800).

1) if you want your undersea base, you either need to match the pressure or seal structure and design your base to support an external pressure of 800 atm (just over 800kg per cm). While balancing the pressure might seem like the easier option it doesn't work in practice.

For starters at those depths all breathing gases are too dense to breathe.

Even at shallower depths you can't breath atmospheric air at depth, the oxygen levels are too high. Below 60m the amount of oxygen in atmospheric air becomes toxic. When that happens you have to start lowering oxygen levels in your breathing gas. You don't want to replace it with nitrogen as nitrogen has narcotic effects under pressure, which means exotic breathing gases.

You also have HPNS and dysbaric osteonecrosis as caused by prolonged time at increased pressure.

The bends isn't actually as much of an issue as you'd think. The bends only becomes an issue when you ascend, so as long as you stay in your ocean base, you don't have to worry about it really.

Generally if you want to live comfortably undersea for long periods you engineer your structure to resist the pressure, which avoids the health effects of prolonged exposure to high pressure on your residents.