There is no “death” functions in ESX. That is handled through baseevents. Base events calls a client event when you die, ESX hooks into that and then handles it’s death from there. The only thing ESX does out of the box if the player dies is prevent them from accessing the inventory. Not sure what “isn’t working” about that for you. As long as you have base events active on your server every should be fine.
As for admins driving vehicles, look into Fax Core - Ace Based Permission System, Including Blacklisting of Cars, Peds & Guns [Fax-Core] [2.1]
Also, like @hallux said, your best bet for ESX-related support is either opening a GitHub issue on the resource in question, asking on the release thread if it exists, or in the ESX Discord.