A creature with a speed of zero cannot stand up.
The rules for being prone say:
You can't stand up if you don't have enough movement left or if your speed is 0.
To move while prone, you must crawl or use magic such as teleportation.
A creature with a speed of zero cannot stand up.
What if the monster can teleport?
This question establishes that teleporting technically does not help with standing up, but gives a possible solution abusing the falling rules. Szega's answer says:
But there is a way around this. (Inspired by this answer.)
At the end of a fall, a creature takes 1d6 bludgeoning damage for
every 10 feet it fell, to a maximum of 20d6. The creature lands prone,
unless it avoids taking damage from the fall. (PHB 183)
If you do not teleport onto the ground (and there is no such
requirement in misty step), then you will obviously fall and
therefore follow the rules cited above. If you do not teleport higher
than 10 feet, you take no damage and therefore do not land prone,
leaving the only option of on your feet. Since you do not move
horizontally, you cannot teleport that far away (deducting 5 feet
seems a reasonable approximation).
So to answer your use case, none of 1, 2, or 3 are exactly correct, though 3 is probably the closest.
Homebrewed problems require homebrewed solutions
It's a homebrew monster. If you're the DM, just fix it. Make it immune to the prone condition, or just let it stand up when it teleports.
I can understand wanting to be faithful to the RAW representation of a monster when the monster is in published material. But this is homebrew. The point of this monster is to bring a unique challenge and unique mechanics to the encounter. Just fix it so that your players don't turn a really cool encounter into a juvenile cow-tipping session (unless that's what you're into, which is just fine too!).