Records
Is there a way to see some of the records of this site?

For example the longest webm, the post with the highest score, the most favorites, the shortest upload, the most popular genga, most popular copyright/terminology/artist and so on. I would also like to know what the most popular scene of each year was and how many new uploads there are each year.

I think stuff like that would be really interesting to know and worthy to keep track of :)
Popularity is fairly easy to track at least, you can just click 'Popular' at the bottom of the page https://sakuga.yshi.org/post/popular_recent?period=1y

As for upload count, the options are limited but you can check by copyright (https://sakuga.yshi.org/tag?name=&type=3&order=count ), animator (https://sakuga.yshi.org/tag?name=&type=1&order=count ) and terminology/tags (https://sakuga.yshi.org/tag?name=&type=4&order=count / https://sakuga.yshi.org/tag?name=&type=0&order=count ).
1. For example the longest webm - Can't do that since the booru doesn't store upload lengths afaik.

2. the post with the highest score - liborek's post: https://sakuga.yshi.org/post?tags=order%3Ascore

3. the most favorites - Can't see a way to do this

4. the shortest upload - see 1.

5.the most popular genga, - https://sakuga.yshi.org/post?tags=order%3Ascore+genga+

6. most popular copyright/terminology/artist and so on. - See Kvin's post

7. I would also like to know what the most popular scene of each year

2013 - https://sakuga.yshi.org/post?tags=order%3Ascore+date%3A2013-01-01..2013-12-31 (The Booru only started on 2013-08-16)
2014 - https://sakuga.yshi.org/post?tags=order%3Ascore+date%3A2014-01-01..2014-12-31
2015 - https://sakuga.yshi.org/post?tags=order%3Ascore+date%3A2015-01-01..2015-12-31
2016 - https://sakuga.yshi.org/post?tags=order%3Ascore+date%3A2016-01-01..2016-12-31
2017 - https://sakugabooru.com/post?tags=order%3Ascore+date%3A2017-01-01..2017-12-31
2018 - https://www.sakugabooru.com/post?tags=order%3Ascore+date%3A2018-01-01..2018-12-31
2019 - https://www.sakugabooru.com/post?tags=order%3Ascore+date%3A2019-01-01..2019-12-31

8. how many new uploads there are each year.

2013 - https://sakuga.yshi.org/report/post_uploads?start_date=2013-01-01&end_date=2013-12-31&limit=29&level=
2014 - https://sakuga.yshi.org/report/post_uploads?start_date=2014-01-01&end_date=2014-12-31&limit=29&level=
2015 - https://sakuga.yshi.org/report/post_uploads?start_date=2015-01-01&end_date=2015-12-31&limit=29&level=
2016 - https://sakuga.yshi.org/report/post_uploads?start_date=2016-01-01&end_date=2016-12-31&limit=29&level=
2017 - https://sakugabooru.com/report/post_uploads?start_date=2017-01-01&end_date=2017-12-31&limit=29&level=
2018 - https://www.sakugabooru.com/report/post_uploads?start_date=2018-01-01&end_date=2018-12-31&limit=29&level=
2019 - https://www.sakugabooru.com/report/post_uploads?start_date=2019-01-01&end_date=2019-12-31&limit=29&level=
2020 - https://www.sakugabooru.com/report/post_uploads?start_date=2020-01-01&end_date=2020-12-31&limit=29&level=

You can also see what's popular by month:
https://sakuga.yshi.org/post/popular_by_month
Maybe everyone knows these already, but I'll just add some search tips, since some of this is about searching.

1. You can use - (minus) as Not.
A couple examples:
https://sakuga.yshi.org/post?tags=-presumed+-artist_unknown
https://sakuga.yshi.org/post?tags=impact_frames+-animated

2. Default search mode is intersection, but you can change to union by prepending ~ (tilde), e.g.
https://sakuga.yshi.org/post?tags=~metropolis+~giant_robo
or, both modes at once
https://sakuga.yshi.org/post?tags=~sports+~dancing+shinya_ohira

3. For searching by score and other numerical things, you can use comparison operators, like <, >, <=, >=.
Example:
https://sakuga.yshi.org/post?tags=score%3A%3C10+width%3A%3E%3D1000+animated

Surprisingly, this also seems to work with dates, e.g.
https://sakuga.yshi.org/post?tags=date%3A%3C2014-01-01

However, trying to search for something like "score:>10 score:<15", expecting intersection, i.e. all posts with score in range (10, 15), doesn't work as expected... I think it ignores the first one.

Also, for something like "~width:1500 ~width:1000", expecting union, i.e. all posts of width 1500 or 1000, again doesn't work as expected.
Wow, thanks a lot! I didn't know there are so many specific search options, that's really helpful and very interesting to know!