I'm on level 2 of catacombs at the moment. One of the rooms (see: attached image) was FILLED TO THE BRIM with skeleton warriors. Not only that, there's also a spawn point in the eastern part that keeps spitting them out even while you're inside. I must admit I got a bit frustrated after fighting them for 20 minutes.

Question: does that happen a lot in the game? I just finished the EotB 1 and while some enemies do respawn, it's nowhere near as bad as the example above.

Enemies do respawn on most levels, yeah, but the room you're talking about is filled to the brim with skeletons right from the get go. In my opinion it's one of the hardest parts of the game, especially if you didn't import a party from EotB1.
It's incredibly time-consuming trying to clear those guys out and staying alive in the process.

From what I recall it's generally not as bad on other levels, although there still are a few mean surprises here and there.

They are building a skeleton army and this is where they keep some of it. Sadly you have to fight your way through. Kill a few, retreat to the upper level, rest and come back. Once you've cleared the area, you're good. A few skeletons do spawn occasionally, but they are no trouble.

Those lousy skeletons and bunch of evil clerics are nothing in comparison to what you'll get before entering the Frost Giant Prison. I still don't know how I was able to reach it, twice.

I think there are only 3 heavy spawn areas in the whole game, the one mentioned in OP, the never-ending army of Aerial Servants on Azure Tower Level 4 and the unforgiving spawn of Mind Flayers on a last level (plus there is an optional trap).
It is possible to avoid Mind Flayers completely, odd design.