Firstly, yes. You'll find a lot of pictures like that if you go looking for Giger's stuff. Just avoid the 'penis forest' painting and you should be fine. If not, don't say I didn't warn you about it.
Secondly, Rex would be hugger-bait. They could be swallowed whole and implant, wait for the things to sleep and hug or simply burn through the neck and do it. They're tenacious.
The same applies to Predators. Even if a precious few could survive, they can't stay awake forever and most would not be strong enough. How are a bunch of 'Cave Predators' going to survive simple tactics, like a facehugger swarm, in any case?
Heck, if this Predalien is anything to go by, all it would take is one of them to go the obvious way, even if they could beat 'conventional' versions.
The only way they might be able to co-exist on the same world is if geography hememd the Aliens in, but they seem perfectly able to traverse just about any environment. Perhaps even liquid magma, if the lack of damage molten lead did, is anything to go by.