Yes, you can connect accounts. Typically (except for Twitter), they will provide you with the user's email, which you can use to connect accounts.
Yes, you can overwrite the default scopes.
http://laravel.com/docs/5.1/authentication
Before redirecting the user, you may also set "scopes" on the request using the scope method. This method will overwrite all existing scopes:
return Socialite::driver('github')
->scopes(['scope1', 'scope2'])->redirect();
Yes, I believe you can update certain information, but you should look at the social network's API for that.