Are there items that make it easier for low level pets to fight higher level opponents?
Stat boosters and training? The new system has made it so that higher level opponents can not be defeated just by equipping a low level pet with a strong weapon, in fact strong weapons can not be used by low level pets, the weapon has to be of the same tier or lower that the pet to be used you do need to train and invest in appropriate-for-your-pet weapons. has some great guides in the Battle section of the forum.
I have been training, but I feel like there is an item or something that heals your pet each turn.
There are... Healers? Like the , but for a full list you need HERE, though with the BD revamp the list is a WIP, there are also Potions. The Healers still obey the tier system however, the Grimfruit is Tier 4, so nothing under that can use it.