You will need at least two licenses, one from MPEG-LA and one from HEVC Advance. MPEG-LA publishes a list of patents so you can see if there are any covering your country. In addition, HEVC Advance also licenses based on the total revenue your content generates for your website.

tl;dr yes, if you don't pay for licenses for all of the required patents.

TL;DR, maybe! From the main BPG website:

Licensing

...

Some of the HEVC algorithms may be protected by patents in some countries (read the FFmpeg Patent Mini-FAQ for more information). Most devices already include or will include hardware HEVC support, so we suggest to use it if patents are an issue.

http://bellard.org/bpg/

>hardware HEVC support, so we suggest to use it if patents are an issue.

This will not save you from the HEVC Advance content fees, which are a percentage of your website's total revenue related to the images.

So, for websites that do not charge -- it is zero ? (ex. wikipedia)

If so, almost sounds like the reason to use it on free websites, so paid for ones do not steal your images