If you were unfortunate enough to fall into a 1-M sun black hole, you would be killed by tidal forces long before you reached the event horizon. Assuming that somehow you could survive the descent, you would see clocks far from the black hole keeping slower and slower time, until as you neared the event horizon they appeared to stop altogether. This is a gravitational redshift caused by the photons losing energy as they escape the gravitational field. Seen from the outside, the photons would be infinitely redshifted to zero energy as you reached the event horizon. All of these effects are consequences of general relativity.
Nobody really knows.
This endpoint is called a singularity . If we observed a star in orbit around a black hole from a distance, we would not see the black hole, but we could see the star's orbital motion and calculate the mass of the unseen companion , just as astronomers routinely do in the case of ordinary faint companions. Furthermore, such strong gravity exists close to black holes that any matter falling into them undergoes terrific acceleration. So x-ray and gamma ray telescopes search for black holes.