How can I check my partners health?
Is there anyway to see how much health my partner has?
Does their health automatically recover? So I basically want to know if I should worry about healing them and if so, then how do I know when to heal them?
Your solo partners are on autopilot. They'll show a round red warning icon above their heads when in trouble, but they'll rarely need help at all on lower difficulties (even when inundated). It's actually hard (impossible?) to down your partner on lower difficulties.
You can't check their health bar status, and their health will automatically recover when out of danger. If your solo bot partner goes down often in higher difficulties, you can take a pill/herb or First Aid Spray to heal you both at the same time. I'm not crystal clear on whether bot partners are just useless or "at low health" on high difficulties.
In co-op, your partner's tag/name will turn red to indicate low health, but it's usually best to ask them if they want/need the help first.
Using herb pills or First Aid Spray (FAS) near your partner (solo or co-op) always heals both of you the same usual amount (one block for pills, full for FAS).