Is it possible, for a 1st Gen tag, one you either tamed or won on one of the wheels, but is it possible for them to carry more than one Mutation in one slot? Like, it'll say one thing, then you breed with another 1st gen tag with the exact same mutation, neither one altered with a mutation/gene philter, and then the offspring comes out with a completely different Mutation in that one slot?

Yes, its possible that tagged pets may carry recessive genes.

This Frog Song Ny'vene is an example:
https://www.sylestia.com/view/pets/?petid=693573

Her image URL is:
https://www.sylestia.com/image_builder_pet.php?species=ny'vene&breed=sylesti&gender=female&gd1=FH&gd2=NN&gd3=NN&md1=NN&md2=NN&md3=AB&ec=f1ef0a&c1=17430a&c2=f0f4a6&c3=045205&gd1c=75a23e&gd2c=102a04&gd3c=f6f673&md1c=216f24&md2c=156b19&md3c=f8f266&maturity=648&owned=1&size=250

Both gene 1 (FH) and mutation 3 (AB) are visible.

In relation to gene 1, F stands for Crested Lizard while H stands for Saber-Tooth. Because Crested Lizard is dominant, Crested Lizard is the one that's visible. If you were to breed this Ny'Vene with another Ny'Vene with HH for gene 1 as an example (of any other combination of less dominant genes), there'd be a 50/50 chance that the offspring would show Saber-Tooth and not Crested Lizard.

The same thing applies to mutation 3. A is Essence of Flames, B is Essence of Storms. Flames is dominant so that shows but Essence of Storms can be passed on and may show up depending on the breeding partner.

Edit: Just to clarify too, a breeding partner could also have a recessive gene, meaning that if both partners contributed their recessive gene (a 25% chance) the most dominant of the genes contributed by the parents would show.

Thanks for clearing that up, Wander! I was really confused on why I had two different PB's with genes/mutation that neither parents have. ^^ Thanks again! =3

You're welcome :)