Firstly, when your character is devoured, do you discard their clue tokens and money as well? The rules only mentioned discard all cards and keep all trophies, but it made no mention of clues and money tokens. I have a feeling that thematically, you would discard them as well but I'm not sure.
Yes, discard your money and your clue tokens. Your new investigator will get money and clue tokens if its in his/her starting equipment.
Secondly, when the only investigator in Arkham is at the hospital or asylum, and the movement for the hound is triggered, does the hound stay where it is or move to the nearest street to the investigator since it can't move onto the hospital or the asylum?
The Hound stays in its current location.