World clock
The current time in as many places as you want to add, all rendered from a single instant. Shift the slider and every clock moves together, which is how you find a meeting time that is not the middle of somebody’s night.
How to use the world clock
Every clock here is the same instant rendered through the browser’s own time zone database, which is the only approach that stays correct. A hand-maintained table of offsets goes stale the moment a country changes its rules — and they do, several times a year, sometimes with a few weeks’ notice. Daylight saving is also why "the difference is six hours" is unreliable advice: between March and April, London and New York are five hours apart rather than the usual four, because the two switch on different dates.
Questions
Yes, per zone and automatically, using the time zone database your browser ships with.