When does a JR Pass go active?

If I purchase a JR pass at the station, is it active the moment I purchase it and the countdown timer starts immediately? Or does the countdown timer only start after my first swipe through a train platform gate (which could be several days after I purchase it)?

Also, to confirm, all online sales of JR Pass require an active date in advance (which cannot be changed once selected) and all vouchers are delivered via paper mail only?

If I purchase a JR pass at the station, is it active the moment I purchase it and the countdown timer starts immediately?

You select a start date at the time of purchase, which needs to be a day within one month. Note that the sale if the pass at train stations will end on September 30, 2023.

Also, to confirm, all online sales of JR Pass require an active date in advance (which cannot be changed once selected) and all vouchers are delivered via paper mail only?

No, to the opposite. Most do not. The only website that requires you to select the start date at the time of purchase is the official JRP website. All others will provide you with a voucher, which needs to be exchanged to a real ticket, and the start date is fixed at the time of exchange. I think all vouchers are paper.

Just to add to Uji's excellent answer, the printed ticket/pass has the dates of validity printed on it. These are calendar days, not hours. So if I buy something like the JREast Tohoku pass today (30-Aug) I can have it start 12th-Sept and it will show 12/9 to 16/9.

Currently, traveling in another country right now. If they only deliver voucher by paper, this means the only way to get the pass is to by at a Station then, correct? Or is it an email voucher ?

https://www.westjr.co.jp/global/en/howto/train-reservation/receive/

JR is not one company. the systems may differ depending on the company.
the above link is JR west. you can buy a voucher on line.
when you exchange a voucher to a real ticket, they identify you with your passport, credit card (you must have it physically) which you used when buying, and some numbers which you decided and/or they sent when buying.

so, if you buy vouchers from the official sites, I think vouchers are not paper.

If you chose to get the physical paper voucher option (cheaper than the online system) you can easily have it delivered to an address in Japan such as your hotel. This is assuming the pass actually is cheaper/more convenient than just booking ordinary tickets.