I have read a lot about Akonadi, always looking for something, about a would like to ask now.

For example, if I will migrate all my resources in Kontact to Akonadi, and configure Akonadi on all my computers to use one MySQL database, then all my Kontacts instances will be automatically synchronized?

Akonadi's task is to provide a universal and consistent interface to retrieve content regardless of the source. Akonadi does not store the content itself, but merely caches it, including any changes you make when a store cannot be updated ( for instance when you are offline, and thus cannot connect to a IMAP server )

As such, what you need to do is store the underlying sources on one machine and have the individual Akonadi instances access them there.

Akonadi is not a server in the sense of clients being on different machines, it is a user session service.

Configuring the same database for more than on server could get the database into an inconsistent state, no idea of MySQL handles this implicitly.
It is not a supported mode of operation of Akonadi itself.

What you most likely want to have is a Groupware server, e.g. Kolab

Cheers,
_