From what I can infer from the treatment given to Wood Elves and Khajiit "employees" in the Thalmor Embassy...and from the blatant racism of the Aldmeri Dominion, is it safe to say that the Altmer have enslaved the Khajiit? Like, have they taken them as household servants and actions of the such?

Also, how much control do the Thalmor have in the client Kingdoms of Elsweyr? Did the Khajiit rule themselves with Lords in Counties? Do they still do so now?

Enslaved? No, but I don't doubt for a minute that the Khajiit (and any Bosmer that doesn't cuddle up to the Dominion) are treated as second class citizens. There's certainly a callous disregard for anyone of a lower position given how casually the poor girl in the party gets tossed in the interrogation room for refusing the advances of that sack of Guar dung Erikur. The Confederacy is a client state of the Thalmor and thus subordinates of Alinor's military and what not. They do probably keep to themselves on a local level...maybe. I don't know, the 4th era Thalmor are incredibly aggressive as is.

One does wonder if a Mane was born since the Void Nights though. I wouldn't be surprised if that becomes something of a plot line for them later on down the line.