Aliens can psi attack any xcom operative on the field. XCOM cannot do that, they need vision.
Aliens are immune to fatal wounds.
Aliens can see in the dark. XCOM still haven't figured out what flash lights are.
Not sure what version of the game you played, but it's possible to PSI aliens if you know where it was situated and if it didn't move, they don't attack any operatives, they just have much better vision, hide your toons better. I personally saw several sectoid <insert profession> dying from 'grey' wounds, one even died in flight to the base, i think. The problem with PSI was that it had fixed TU cost (it was somewhat alleviated in Pocket PC remake, where it's % based), which made your psykers infiitely more powerful with each 'levelup'.
Small arms cannot shoot through walls without destroying the intervening cover, at least not normally.
What you may be seeing is a graphical bug.
There were several screenshots published in 2012 xcom thread here on the Codex where the player toon shot through a solid wall and killed an alien standing behind it.