Question

Is there option to check that some kind (I’m interested in post-receive) hook is present in some remote repository?

Answer 1

Not remotely from a client.
You need to:

• either have some kind of access to the git upstream repo with said hook
• or know that the hook is made to display some message that you can parse when you are pushing to the upstream repo.

Hooks are very much local to a repo and are not pushed/cloned around.
As such, they aren’t visible from downstream repos.