My pets are fully happy, fed, and they're not currently in any battles yet they continue to not show up when I try to battle these storm creatures!

You may want to read this first: http://subeta.net/forums.php/read/785276/sick-Is-your-pet-unable-to-battle-Look-inside!- And if that does not work then file a ticket! (you can file a ticket if you look above under the subeta tab, then choose ticket)

See above. :)

Were you able to resolve this?

Not yet, Im currently talking with someone.

Ok let me know when this is resolved! Thanks :D