i think pets should be semi permanent, like you have a stable with 3 spaces, oracle only gives you a pet if you have empty space. you can upgrade your pet, you can give your pet extra statuses, like adrenaline, momentum, quintessence. pets are selected from a specialized list. maybe one or two from each element.
immortal
spark?
dragonfly
firefly
parasite
devourer
vulture
skeleton
antlion
gnome rider
abomination
shroedinger's cat
ash eater
fire spirit
charger
firemaster
scorpion
frog
photon
angel
deja vu
scarab
crawler
crysora
maybe oracle gives rare pets of dragon and nymph or otyghs and annubis etc.
pets die if they get killed, or if you dismiss them.
upgrades are really expensive, like ten times the cost of the card or more, quintessence should be like 15K.
you can only use them in pvp 2 or possibly the arranged matches as an option so you can show off to each other.
you should be able to get a 'bonus' from each element, blessing from light, etc.
two pets in action, one on either top corner.
cool idea~ but unfortunately in Elements so many CC spell can mutilate your lovely precious pet with dirty cheap cost.
Those little creature you mentioned can make no big different against FG but large different to PVP.
Or make PVP no pet will be also good.
It's fun, but I'm not sure this will be what game designer want, Pokemon Elements