1. No
2. No
3. Yes/Never tried, but likely No.
Hevnoraak may notice His name being used by Necromancy and be able to provide an answer to 4 that is definite. Cider has done a similiar Roleplay and also may provide a Butter Answer
During Diplomatic Immunityhttp://www.uesp.net/wiki/Skyrim:Diplomatic_Immunity#Hooded_Thalmor_Robes_Method.
All others are not possible unless you have mods (of which I know of only one that might allow you to do so in those other instances)
It was clearly intended for the character to be able to disguise themselves in the embassy. To a degree anyway. If you play as Argonian or Khajiit and try sneaking around in Thalmor robes, the guards will make comments like "Is that a tail?" I just wish they had expanded that out into the rest of the game world, along with the other faction armors.
Yeah it's really a shame you can't properly pass for a Thalmor.
Doubly sad that Thalmor wasn't a joinable faction for those of elven races.
If you are on PC you can add player to the thalmor faction and they won't attack you and revert to standard faction npc dialogue. I did this with a character and it is a nice little change up in the game. You can pretend you from another faction within the Thalmor that is infiltrating Skyrim for their own reason, or that one of Elenwen's superiors sent you because they were unhappy with her progress in Skyrim or they also mistrusted her. I envision a society like the Thalmor's being rife with infighting. It is also the same thing the Nazi's would do, send secret SS agents disguised as regular officers to keep an eye on the other branches of the military. When at the Thalmor embassy on the main quest, I sort of sneaked around to make it feel realistic. Once you add yourself to the faction though there is no way back I know of, but regular people don't treat you any differently.