What are the notification services for new publications on various sites?

Question

Automation

First, I'll describe the problem. I don’t have much free time to view topics of interest to me on the Internet, and when it appears, I do something like this:
I go to YouTube and other resources with subscriptions and see if there are new videos, statuses, etc. in my subscriptions.
I go to a few forums that interest me and look through just a few topics that are useful to me for new comments.
I go to several blogs and look for new comments on posts that interest me, and also look for new posts on topics that interest me.
To do this, I simply open tabs in the browser from the list of bookmarks. All this is not very convenient, because. for example, if I open a forum topic at a certain place on a certain page, then after reading new comments and moving to another page, I have to change the bookmark in the browser to start from this place later, etc.
The problem is exacerbated by the fact that only half of the sites I'm interested in have RSS and Atom feeds, and on even fewer sites these feeds are made "in a human way" (for example, few feeds take into account the settings of my "local" accounts).
It would be great to find a service where I could specify in my account a list of URLs that interest me and, possibly, for each URL, specify some more data for filtering, so that in the future this service would do all the above work instead of me t.s. in the background a couple of times a day:

• I looked through the pages for changes / new information (changes in the entire text or a specific fragment: prices / descriptions / etc., new comments, etc.).
  
• If a new page appeared in the forum topic of interest, I would go through it and count all the new comments.
  
• Would do something else useful to find updated content :)
  

And then I could go to my page on such a resource and immediately see where something new has appeared recently in the form of a list of links with descriptions of changes and go directly to the most interesting resources with updates.
If anyone knows of such services - give links to them, I would be very grateful.
UPD 2017-04-17
Thanks for the answers.
At the moment there are many interesting options in the answers, but there is not one that would suit me.

Answer 1

I myself use the Distill Web Monitor chrome extension , just for such cases.
You can select the part of the page and the frequency of tracking changes.

Answer 2

RSS

Answer 3

Inoreader + Rss, covers a wide range of described scenarios.
You were offered the conversion of different sources into standardized feeds (RSS), then you can display and catalog them in any convenient interface in one form / place (inoreader / Feedly / etc).

Answer 4

The service allows you to create RSS feeds from any web pages. In fact, Feed43 provides a universal RSS-based API to any site, any page, and even any part of a page.

https://habrahabr.ru/post/37780/
+More similar ones:
https://www.google.ru/search?q=yahoo+pipes+alterna...

Answer 5

I use google alerts . in a nutshell - creates an rss feed for you for new search results for the entered phrase.
you can mess around with attachments site: inurl:and so on.

Answer 6

Twiner is a mobile application for Android.
Aggregator of various user content. You collect all your subscriptions in one application.
Convenient to use. Now only youtube channels, but in the near future it is planned to connect other social networks. media.