Is it possible to set a notification (push-up, e-mail) when a new post or subject is created? If so, where can it be set?

You'd have to follow each forum/etc.

I have described the need incorrectly, I'm sorry

We have an IPS based forum;)
I would like our moderators and employees to receive a notification every time a new post is created so that they can check the correctness of the post immediately and possibly respond.
How and where to do it?

Still the same answer. 

If your site really runs this way that EVERY post is going to be checked, then you might also want to consider using moderator approval for posting. That way, there will be notifications and the post can be checked before it is even published. 

Sure, thank you for the answers.

We start and have a small forum, several posts a week.
Nice idea with moderation, but it will slightly make it harder for users to work.
It is a pity that it is not possible to set notifications, push info, e-mail or RSS for the Administrator, operator, moderator or selected users.
For large forums, this is not very useful, but for small ones - I think it's a nice idea.
Then employees do not have to worry that they miss the answer to the user's question and do not have to refresh the site all the time.

RSS from an Activity Feed should work.

Yep, I think this is simple solution