Your own time zone is outlined below.
Yes, automatically. Times come from your device’s IANA time zone database — the same data your phone’s clock uses — so summer time in Europe, DST in North America, and the southern-hemisphere reversals in Sydney and Auckland are always applied for today’s date, not a generic offset.
Not every zone sits on a whole hour: India runs at UTC+5:30, Nepal at UTC+5:45, Newfoundland at UTC−3:30. The offset under each clock shows the real value, whatever it is.
Over 4,000 by name — every city of 150,000+ people plus every national capital, matched as you type (accents optional: “Sao Paulo” finds São Paulo). Anything smaller: type the nearest big city in the same country, or an IANA zone name directly — from Kiritimati (UTC+14, first to see the new year) on down. Your additions are stored in your browser’s local storage and never leave your device.
It ticks off your device’s own clock, so it’s exactly as accurate as your computer or phone. If your device syncs time over the network (nearly all do), you’re within a fraction of a second.
Entirely in your browser. Dates you type are never sent anywhere — there is no server doing the math, no analytics watching you do it.