Email address is required by Joomla. A user can not register without one. Joomla user store it self will reject the user store and fail the registration.

Is there any way at least i can disable the "Please enter a valid email address" check? So that the users might put words inside, like "none" or "/" whatever...

No, it's an email field so it has email validation attached to it that can't be disabled.

Second option would be to put default value for the email for some dummy address like " user@domain.com", but then again the system asks for unique e-mail address for each user, is there override for this?

No, the email address must always be unique. You could use CB Auto Actions on the registration form display trigger with a Code action and Method of jQuery to generate a random email address using JS functions then pushing that value to the input.

Third option, perhaps there's a way i can automatically fill the email field with username (from the username field) @domain.com?? Maybe with ab auto actions or cb query?

Validation would reject it before you could do this. You could try the before registration trigger and populate email field using a Code action with Method set to PHP then populating the POST global, but I've no idea if that'll work.

Joomla it self really is not designed for what you're trying to do. That issue needs to be addressed first. You need either an extension or to modify Joomla it self so emails aren't required, but I doubt that can even be done without modifying core Joomla code.

Third option should imho be possible with a bit of CSS and javascript jQuery e.g. in your site template.

You would still end up with either invalid emails, or would need a catch-all email account on the chosen domain.com, as Joomla and CB may send workflow emails.