Quote from: CaptainArmenia on July 20, 2016, 07:21:06 PM

On one post with rules and guidelines I saw a table with limits for each member level. The levels for PMs were really low, I think it said you can only have 3-5 "max PM recipients" when you are starting out, and even higher level members have very low restrictions. If I understand correctly, this means you can only send a PM to several people, and then you can't PM people anymore, am I right? If I am, can someone tell me possible reasons for this rule on the forum, is it because people don't PM each other at all and higher limits are not needed, or some other reason?

It's the number of users you can send a single PM to.
For example, if you want to have a discussion with two other users, you would have 2 "PM recipients".
The maximum recipient number prevents newbie accounts from writing spam/advertising PMs to 100s of other users in an attempt to circumvent their PM/Post time-limitations.
There's no maximum number of PMs you can write another user, you can PM them as much as you want, as long as they don't block your PMs.

Quote from: CaptainArmenia on July 20, 2016, 07:21:06 PM

Another question. Is there a feature to "go to fist unread post" on a thread you already visited in the past? Starting with the first post page is annoying, especially if there are dozens of post pages on a thread? If this feature is available, please tell me where it's hidden, I'm just not seeing it anywhere.

The forum itself doesn't have a feature like that, but IIRC there's a (user-)script with several additional features, that one including.
Don't have the link handy though, maybe someone else does.

Quote from: CaptainArmenia on July 20, 2016, 07:21:06 PM

The main question is about notifications. Is there a way to see notifications about new posts in the topics you participated, or about any posts when someone quotes you, or tags you? Is tagging even practiced here (I haven't seen it yet in posts)? What I mean by notifications, of course, is not receiving countless emails, that's uselees, but a regular notification icon somewhere with a number of alerts (new replies, quotes, etc)? I just don't see it anywhere in the interface?

There are email notifications which you can set up here -> https://bitcointalk.org/index.php?action=profile;sa=notification
Besides that, there's the "Show new repiles to your posts." list, which you surely already have found.
Further, no features are implemented in the forum, so no, tagging isn't possible and there's currently no way to know if/when/where someone quoted you.