I'm not at all a native speaker, but I'm fairly sure broască means frog as well? Is this just a particular thing I'm not understanding, or are they normally called frog turtle?
I'm not a native either but I believe it's called "shelled frog", like in German "Schildkröte" ;)
Pretty much this. Note that you can drop the "broască" and just call it "o țestoasă".
Yes, we don't usually say "broaștele țestoase ninja", but "țestoasele ninja" (the ninja turtles).
Also, to unlock the door we insert and rotate the key in the broască (the lock of the door).