If the object is hollow, chances are he will experience little to no gravitational force due to the object (assuming the object is roughly spherical, and even if not it probably wouldn't be that much). This is due to all the gravitational mass from one side essentially canceling out all the gravity from the other side. However, time will pass "slower" for him compared to someone infinitely far away from him, due to his location inside the sphere. It is difficult to explain why without invoking a lot of higher physics, but it deals with the accelerated frames that exist between the person inside and the person outside.

If the object were symmetrically distributed, he would experience no gravity. As for time dilation, I suspect that your answer is "yes", although I'm not sure that the mathematical solution to this situation has been worked out.

Yes, time will pass slower than for someone far outside the object, because he's inside a gravitational well. This is due to general relativity. But he won't feel any gravity--or at least, not gravity from the object he's inside. Both he and the object could still feel gravity from something else, though. It would be just like riding the "Vomit Comet" aircraft, where you get "weightless" for a few minutes but only because the plane you're in is falling at exactly the same speed as you are.