I have all 3 stars for the life giver perk but my life doesn't recharge all the time. It only recharges randomly sometimes. Is this normal? Is there another perk that will make your life recharge all the time and more quickly?

Life giver works, it will not heal radiation damage and for its healing to kick in you cannot be in combat.

out of combat only. I don't think any of the passive heal over time perks work in combat/ shortly after taking damage, except ghoulish when you are being irradiated.

Life giver works out of combat. It's too slow to rely on in combat anyway. Not that stims are in any short supply.

Ghoulish combined with mysterious serum seems best passive healing to me.