In multiplayer runs if one of the players dies but the other one finishes the run alive, is the run still valid?

Yes but the other pov still needs to record the rest of the game or record themself leaving the game

And in multiplayer runs both of the players need to have a timer or only the host/one of them and if it's only one of them does that person need to be alive till the end of run?

nobody needs to have a timer a timer is optional as the run gets retimed after either way