The monsters in certain areas (particularly Northland Forest &
Southland Forest in the beginning) seem to be "set" and once they are
dead they are dead permanently.
I believe this is true for Southland Forest at least (orcs and giant lizards), but not for Northland -- the hog respawns after some time (a couple of minutes). Apart from some regular enemies working like this there's also the Larkhon (guarding the Mines) and the Minotaur (in the White Tower) that do not respawn (understandably so, since they're "quest" enemies).
The monsters in Level 1 of Draracle's cave only seem to respawn once I
leave and reenter the area.
Agree with this, although not all of them respawn, seems like it's only the ones in the area before the pit room. Interestingly enough, it also seems to matter how much time you spend on the level between clearing out all the enemies and reentering -- if I do it in quick succession (i.e., kill everyone, fall down to where I found Lora, and climb back), only one giant rat respawns. If I kill everyone, then wait for a long time and then fall down and climb up again, there are ~4 rats there. So it seems that time is a factor here as well.
The monsters in Level 3 of Draracle's cave seem to respawn at a
constant rate as I travel around the area.
Most enemies do respawn with time, though the interval varies. This happens, for instance, in Draracle's Caves 3, White Tower 3, and Yvel City (during the siege). Sometimes you can stop them from spawning by burning their nests with fireballs (giant bees in Upper Opinwood, flying twin dragons in Mines 3).
Can anyone confirm whether these scenarios are correct, or if there are any more?
There are at least two more scenarios.
Some enemies spawn after a specific trigger done by the player.
For example, a stone monster spawns the moment you mine the first
coal from the wall in Urbish Mines 3.
The other respawn mechanism is spawn spinners.
In some areas, you can enter a "spinner", a tile that spins you around in order to confuse you. For a prominent example you might recall the large room in Castle Cimmeria, level 1, which strips you of the Atlas, makes your compass hard to use and forces you to find four pressure plates in a room full of spinners and pits that end in the Dungeons:
Now, most of the spinners in the game do just that, break your stride and force you to do some rerouting. There are at least two locations in the game where spinners have an additional feature, which is spawning enemies. Notable examples:
Draracle's Caves, Level 2
In Draracle's Caves, Level 2, spinning on the spinner tile denoted with a blue X spawns 1-2 cave people on the red X tile. It seems that it's consistently 2 for the first spin after the area has been cleared out and then either 1 or 2 more for each spin, but they seem to stop spawning after there's about 4-6 of them in the spawn area.
There's also another spinner in the same level that spawns rat people for a change: when you take the Sapphire route, before the first secret wall.
In the area with many one-way secret walls and spinners, some of the spinners seem to generate Dark Army Knights in the target area (red X), so the more you get confused by the game there, the more enemies it punishes you with later on.