Will biological process be disrupted under strong gravitational time dilation? This question is raised by someone I've discussed with, after watching the movie "Interstellar", in which a clip showing Cooper and Amelia landing on Miller's planet near a super-massive blackhole and they experienced quite amount of time dilation due to the gravitational effect. They spent like 20 minutes there and when they backed to the station they found out that 23 years have passed on station (where Romilly waited them for 23 years to return).

It's okay for this conception to be implemented here I believe most people will understand. We will just think that yeah 23 years has passed but they just feel normal, just like a 20-minutes park walking. BUT, no one has ever experienced such a strong time dilation, how could you be sure Cooper "just feel normal"?

I remember reading a book which says if you are rushing directly to center of a blackhole, when you are very very close to the Schwartzchild radius, you may experience a whole lifespan of universe IN A SECOND, in other words, you are rushing to the real end of the world. I really doubt any life could 'feel' that second passing. Anyway, this is an extreme example.

So the question: will biological process behaves normal under certain gravitational condition? If it does, can we feel differently? Does our conscious get used to the normal time flow all life on earth are living with? more crudely, will we die due to the extreme time dilation caused by gravity (provided that gravity affect homogeneously upon us) and if so, how?

An interesting extra: If Romilly could observe Cooper from station and sees a near still 'slow-motion' picture of him, will Cooper conversely see a 'fast-motion Romilly' from the ground of Miller's planet?
Remember this is a theory of "relativity". Now, time dilation due to gravitation effects is rather outside our normal experience. But there are relativistic effects that that you experience all the time.

I'm sitting on a train. Relative to my computer I'm not moving. Relative to the track I'm travelling at 100km/h. Relative to the sun I'm moving about 30 km/s, as the Earth orbits. Relative to a distant galaxy I'm moving close to the speed of light.

But in my frame of reference, I'm not moving at all. So, even though I'm moving at nearly the speed of light, relative to some distant galaxy, I don't notice any slowing down of my watch. My watch is moving with me, in my frame of reference.

It would be the same if you were experiencing intense gravitational time dilation. For example, if you were falling around a black hole. Your watch would be in the same frame of reference as you, so there would not be any observable difference, locally. 

If you tried to stop yourself falling, the force required would crush you. Small black holes have such extreme variation in gravity that your head and feet would be pulled apart by the tidal difference, and if you passed the event horizon, you can never come back. So you would be dead if you tried the experiment in practice. However "gravity" itself can't hurt you, only variation in gravity or your own attempts to act against gravity.