Yes, but this is a disease that infects planets, not actual time. EDIT: Is it me, or is your name said as R on the quotes?
Off-ish-topic: I've always wondered if we really know if all of the quantum-mechanical fields are actually completely uniform throughout the universe. We can't know for sure, we have suggestions that the electromagnetic force is the same, or else we'd see spots of no light though the sky. For the Higgs field, as mass decreases, the orbital speed decreases, which would mean that spiral galaxies and stuff would be orbiting at much slower speeds, are much larger, or wouldn't exist at all, unless the gravitational constant changed, which could be because it's linked to the Higgs field through QFT. On the very largest of scales, we have absolutely no idea that I know of that suggests that the Nuclear forces are uniform. Due to the strange pattern of the layout of galaxies on the very largest scale, what's going on in the middle is anyone's guess.
Universe as we know it cannot exist without time. This universe is based on (sub-)molecular processes which would just stop without time, it allows us to exist. Physics is on an edge, we want to know the reason of gravity, but why stop there and don't ask what the reason of time is? We have to find the smallest functional units which give everything it's properties, and maybe, there is the same for all, maybe we can't find it/them. So if you enter a planets atmosphere wich has no time, it's gameover Divide by 0 error meter/second (e.g. 10/0 = ?). There is no heat since temperature is movement of particles (is time standing still at 0 Kelvin?). But it would be interesting what light does when it enters a no-time-space.
There is a thing call Gravitational time dilation. its when when a object's velocity increases while time decreases. this could mean that the planet in question could be orbiting a denser star or a less-dense star to cause this "slow or fast planet" to be possible.
Ah, yes, I am familiar with the concepts you are referring to. (Although to say 'there is such a thing' is to put your full and utter trust into Einstein's theories, which may or may not be a good idea) So, theoretically, a planet with 'no time' could simply be moving at a theoretically infinite speed - which, of course, provides its own complications, but hey, like we've said, it's a game.
No time could also means that half of the planet is always in the dark while the other side is always sunny.
http://playstarbound.com/suggestions/?c=4&pg=5 Don't know how to get a link to upvote/downvote, but thats the link to it.