How to autorefresh Calc sheet

I’m trying to create a countdown sheet, with multiple dates. But it’s really annoying to having to use F9 every time I want to see how much time is left on the countdown. Is there someway for me to autorefresh the sheet every second or so?

Also, as a bonus question. Is there any way to set up multiple timezones in the same sheet?

No. There isn’t a specific timer of the kind, afaik.
The only solution I know relies on user code. BASIC, e.g. has the Wait statement. However, I would dissuade from a continusously running routine of the kind. You may write a stopwatch routine with start/stop button or the like.

I don’t know of any time zone assigned to a spreadsheet. You simply have system time. If you want to get the time one standard zone to the east e.g., simply use =NOW() + 1/24.
Be sure to note that NOW() also has an integer part reperesenting the date.
I you need time-only, use =NOW()-INT(CURRENT())
Using BASIC you should also know that the function Now() there only resolves the time down to seconds. If you need fractions of seconds yoy must use the Calc function NOW() -and in advance create a FunctionAccess object to be able to do so, as it is demonstrated in the example attached below.

Extra bonus:
A look into my toy box relsulted in the attachement below. (I needed to kill a little bug first.)