Panic doesn’t make people shoot their teammates in the mod, it only makes them hunker down. It happens often with green troops, but it’s rare among troops that have gained a few levels. There are also various mechanisms to buff will within a mission.
As far as HP goes, it keeps lesser aliens viable for longer, which makes the encounters more diverse (ie you can still encounter thin men in later missions and they’re weak but not a joke). The alien has to research HP upgrades, so if you can inhibit his research you’ll slow the rate of the HP gain.