Is it safe to have your active pet exploring, then you click pets? You change your active pet and enter the new one into an island. Would it explore when the other pet wasn't active, Or would it do the Synchrnization thing? 

It is safe to click pets into another tab if you are simply going to look at the pets without looking at their profiles, however say I was exploring with Careful Wishes, and in another tab I viewed Blackheart's profile, it would synchrinize on the island if you went back to that tab. But Careful Wishes would still be on the island until I made her active again and finished exploring with her. 

So, I have a pet in level 8 island and I don't want him to leave. He's in there regaining energy. I want Gondalorn to explore. so do i get him active and click explore?

Absolutely. When you have another pet active, your first pet will not leave the island. You click Gondalorn and it will take you to a new island in explore, without affecting your other pet's island.

Thanks!!!!! How do you post an image? I can't do it.

Now that, I am unsure of xD I know you have to screenshot your screen and then paste it to paint and save it as a picture and then you attach it in Browse...