A couple of them, one of the characters works as a doctor at one, another is a patient at one. And it's in the 1800s, so the patients are treated horribly
It really depends on what you mean by excessive. Vlad the Impaler was brutal. Vampires live for blood. There's a scene with blood splashing from either side of a room but that is the most you see in one scene. Not much gore though.
A character called Renfield has Renfield Syndrome. Other characters are clearly traumatised, and are suffering from that, though it's not a clearly identified mental illness.
I'm going to say yes, though some of it is mostly a metaphor for SA. John is first harassed by Dracula, then assaulted by the three wives, Lucy is assaulted by a wolf-vampire creature, Mina is assaulted by Dracula. All of these are committed by using vampiric powers to put their victim in a trance-like state