Question about GB mirror matches.

Lets say two players both using Gladiator Beast decks are playing against each other, during the battle phase, their monsters both survived attacks, e.g murmillo crashing into a facedown hopolomus, am I correct to say that the turn player has the priority to tag out first?

Also, if I reborn an opponents GB and attack, then tag out with it, it returns to his deck but do I get to special summon another GB from mine?

yes turn player monster tag first.

you return his gb back to his deck and special summon one from your own deck.

Hmm okay. Thanks.