What happened to Mrs. Agreste
This is a theory of what happened to Adrien's mother. Okay I was watching Batman and Robin, and the Batman series and one of the main villains Mr. Freeze had a wife named Nora who was deathly ill so he kept her frozen or preserved in some machine til she could be cured.
So my guess is (if Hawkmoth turns out to be Gabriel) A year ago, Mr. and Mrs. Agreste go to Tibet (Tibet was seen in his safe) which happens to have many deadly illnesses, Mrs. Agreste contracts one and falls into a coma and the doctor informs Gabriel that there is a small chance of her ever waking and suggests to pull the plug.
Refusing to lose her, Gabriel takes her back with him to Paris and keeps her comatose body contained in a machine that keeps her alive while he becomes the super villain Hawkmoth so he may use the ultimate power to bring his wife out of her comma.
I know what you're thinking, why wouldn't Adrien or media or anyone else know about this? After all the Agrestes as we've seen in the show are famous. Well what if Mr. and Mrs. Agreste were previously a super hero team much like their son and Marinette but had to take a break from it after having a son? But Master Fu probably asked them to preform a secret mission in Tibet which required their miraculouses and they probably sent Adrien to some overnight lesson or something to avoid suspicion from him, this would explain why no one knew about the trip or what happened to her.