harry potter - When was Hogwarts founded?

This is going to be a really short answer.

If Professor Binns said Hogwarts is over 1000 years old then I would estimate Hogwarts was built, at the latest, in the year 991, which is 1001 years prior to 1992.

The following is my (educated?) guess: Hogwarts is older than 1000 years old, but Binns does not say, "As you know, Hogwarts is not over 1100 years old ... " He says 1000. So I'm going to posit Hogwarts was built between the years 893 and 991. This is over 1000 years prior to 1992, but not 1100+ years prior. The existence of Hogwarts during this time frame would also have allowed for Merlin to have been a student at Hogwarts, if you consider Merlin to be of the Medieval era (there are different dates for Merlin's existence).