Yes, I am pretty sure (I've done it a couple of times but it's been a while since the last... anyone need a heat shield assembly, super cheap?

) that with the spare tire in place you may not be able to reach the couple of small screws or bolts that hold the bracket of the heat shield in place. Once you remove the spare, it's child's play to remove it - but be safe and still place a couple of jack stands on each side of the chassis before sticking your head and body down there.
I don't have a trailer hitch, but if by "265" you mean a 265/65R18, it will probably get in the way of the hitch just like a 285/60R18 spare does. Diameter-wise, the two are about the same.