Before my Father went into an assisted living facility, he put me on his personal checking accout as right of survival. He has been diagnosed with dementia and now has a conservator managing his finances. Upon my fathers death is the money split between me and the conservator (who also manages his trust)?

Depends on if the State goes after that money first if you aren't paying his expenses there. In VA the state is aggressive about recouping their expenses when someone id going to a nursing home and the family isn't footing the bill. Saw several cases personally where the state grabbed ALL assets and the family got nothing. And we are talking estates valued at well over a million dollars.