Hey guys,
There is a new plugin to keep your user records synchronize between multiple classifieds!
New user registered, user has changed profile image or just updated "info" section? Not a problem, plugin will stream these changes to other osclass installations and keep them up-to-date

Take a look on demo:
https://plugins.abprofitrade.eu/oc-admin/index.php?page=plugins&action=renderplugin&file=account_sync/admin/accounts.php

Synchronization can also be done between two web pages when one of them is in a folder of the other?
(One website will be here: https://www.domain.com/
and the other website here: https://www.domain.com/test)

@kriskoyk
Yes, it does not matter where is the destination.

After syncing two sites, is the logged in user of one site automatically logged in to the second site as well?

@kriskoyk
No, because session & cookies can only be relevant to 1 server (1 domain).

If a site works inside another site's folder in this format (www.domain.com/site2) and with separate databases, then it is possible for the user to appear as logged in to both sites, after logging in to only one of the two?

No as session get unique ID based on base url.
You would need to modify this and use just domain as identificator and allow cookies to be domain based (with sessions).
Then it could work.

I did this test: On the domain.com site I installed the second site (test) in a folder (domain.com/test) and the synchronization works perfectly without doing anything else.. From any site I log in or register a user in a minute I am connected to the other as well. Any change I make on one (domain.com) is updated in a minute on the other site (domain.com/test). I hope these settings are correct and there will be no problem.

Sounds great