You can’t put more than one +1/+1 counter on any one target using the support action.

If a spell with support has other abilities that target creatures, those abilities and the support ability can target the same creature.

If Gladehart Cavalry dies at the same time as a creature you control with a +1/+1 counter on it, its ability will trigger.

If Gladehart Cavalry somehow gets a +1/+1 counter, it dying will cause its own ability to trigger.

You gain 2 life per creature, not per +1/+1 counter.

Support can target a creature you don’t control.