What are aliens' movement limitations?

Solution 1:

The reason they were unable to do anything is because the enemy needs to be on an adjacent square on the same plane as the target to use a melee attack. By standing in front of the only broken panel, you were blocking them from entering the same plane as you. In the same vein, you can prevent aliens from leaving a room by creating a meat wall of your operatives on all of its exits - if the doors are closed, they will be unable to attack (having no LoS) or open the doors, since they can't route to a point past the door.

Solution 2:

Aliens movement limitations are the same as your own. If you can open a door / climb a ladder, so can they. However, some aliens (Chyrssalids / Thin Men) are able to "leap" to higher elevations, while the ground based fighters need ladders, etc.

It seems likely that you found a bug with the AI and/or pathing, or otherwise managed to get your sniper to an un-path-able spot, as Chryssalids aren't afraid of small spaces. If you're there, they want to be there too! (So they can whisper sweet nothings down your throat and gestate their spawn in your stomach!)

Sectopods behave the same as ground-based SHIVs, except with more long-range murder.