What can I do with a 8-10 hours layover at the Brussels airport? Can I visit a nearby town? How?
Take a train from the airport to Centraal Staion, and take in the popular tourists sites in the immediate area. There are trains every ten minutes or so, journey time is 25 minutes:
Depends if that 8-10 hours includes the time between checking in for your second flight and taking off. The big name destination is Bruges - it takes about 90 minutes each way by train changing at one of the central Brussels stations. Alternatively there are places in central Brussels it would be worth visiting depending on what your interests are.
The closest major town in the other direction from the airport is the university city Leuven (about 15 minutes away by train). Worth a quick look if you plan to come back to Brussels at a later date. Otherwise, I would go to Brussels, have a quick look at the Grand Place, and check out one of the museums in the immediate vicinity, like the Fine Art, Musical Instrument, Bellvue. 8-10 hours is more than enough time to get a quick overview center of the city, but it would take 2-3 days to get a real feel for Brussels.
You could also easily get to Brugge, Ghent or Antwerp and back in that time, but I would stay closer to the airport and come back to these cities in the future.