Some decent ideas here, particularly #1 which is my personal pet peeve when playing medic. I'd approach some of them differently though.
(3) I'd prefer to have medics stay away from the current shitshow that is jail as I don't think they'd be of much use anyway. Crims would gun them down instantly knowing there's a chance they'll revive cops and you'd have cops shooting medics and getting wanted due to helping crims etc. Not worth the hassle imo.
(4) We'd have to be careful with this, not a fan of having people kill/arrest with no chance of stopping them due to being invincible. Only way I can see this being added is if the player being revived has their weapons disabled for the duration.
(5) I think a better approach to this would be to display a message on the screen, or requiring players to confirm they wish to respawn at hospital, if there is a medic nearby to revive them.