Planets form from disks of matter orbiting around a star as well as some moons form from disks of matter orbiting a planet. If this is going to happen, aproximately how much time will it take?
The answer to the headline question is: No. Most of Saturn's rings are below the Roche limit of about 2.5 Saturn radii. Hence tidal forces will prevent that part of the rings to form a (large) moon.
Actually, part of the rings may be caused by loss of material from some of Saturn's moons, as suspected from observations of Enceladus.
Accretion of Earth is still going on. So any number between millions of years and billions of years of accretion time for a planet can be justified. Half of Earth's mass should have accreted within 10 million years, see this paper.
It will not happen.
Existing moons have orbits that avoid these matter fragments to become bigger, by posing tidal forces into them.