Istanbul Airport runs on Turkish time, UTC+3, and every board and boarding pass uses it. If your connection is tight, the clock at the top of this page is the same time the airport is using.
IST is Turkish Airlines' hub and one of the busiest airports in the world, which is why so many people passing between Asia, Africa and Europe end up looking up the time in Turkey in the first place.
The published minimum connection time for international-to-international transfers at IST is around 60 to 75 minutes, but the terminal is very large and walks between gates can take twenty minutes on their own. Two hours is comfortable; three is safe if you are changing airlines or need to re-clear security.
If your inbound and outbound are on separate tickets you must clear immigration and check in again, which changes the calculation entirely. Allow four hours or more.
With six hours or more you can reach the city. The M11 metro connects the airport to the centre, and Havaist buses run to Taksim and Sultanahmet. Allow at least ninety minutes each way, plus immigration.
With less than six hours, stay airside. There are transit hotels and lounges inside the terminal, and the walk alone will absorb more time than you expect.
UTC+3, the same as the rest of Turkey, with no seasonal change.
About 60 to 75 minutes for international connections on a single ticket, but two hours or more is realistic given the size of the terminal.
Yes, if you have enough time and meet Turkey's entry requirements. Allow at least ninety minutes each way plus immigration, so six hours is a sensible minimum.