Is it possible to heal planimals during fights so they go into combat with full health?
There is no way to heal them like you would with pokemon. When you level up, they will have their health restored but there are no items that will do it for you.
The most useful approach to take is to change the order of your squad so that the injured planimal does not go into combat first and immediately get killed. You may be able to land the final blow with the injured planimal if you move them to a different position in the lineup so they do not go into combat first.