When playing with 5+ investigators, when a gate opens, it releases 2 monsters. What about when an encounter causes a gate and a monster to appear? Or when an encounter causes just a monster to appear? Are these governed by the same rules? Are there any other situations where more than 1 monster appears when playing with 5+ investigators?

Whenever a gate opens, it releases 1 monster—two if it's a (5+)-investigator game. This applies to all things that could possibly open a gate, including encounters, because a doom token and a monster appearing are always tied to a gate opening. In 5+ games, there need to be more monsters to keep things interesting.

Only one monster appears during "a monster appears!" encounter, though: the encounter happens for a single investigator and it wouldn't be fair to make him face more than one. Note that these aren't the same as "a gate and monster appears" encounters, because the investigator will not have to face the monster right away and it stays on the board.

I thought the Gate appears first and thus the Investigator doesn't face the monster?

Yes, that's the point. The dimensional passage opens, and investigator(s) are sucked through it. Then, a monster(s) emerges from the gate ("hey! nice place here! let's take some pictures")

I thought the Gate appears first and thus the Investigator doesn't face the monster?

That's correct. The gate sucks the investigator through so the investigator doesn't deal with the monsters until he comes back through the gate, following normal rules. But the monsters stay there, unlike monsters that appear from encounters.