I'm not a boxcryptor staff member, but I think I can answer your questions.
If I change my boxcryptor password, then I have to export key again? is that right?
Yes. If you change your password, then the key file will be re-encrypted with the new password, so you will need 1) an exported copy of the newly re-encrypted key file, and 2) your new password.
You should also be able to use the old exported key file with your old password to decrypt your files
If I use boxcryptor as local account (without internet connexion), is it possible to revert to boxcryptor used online (with internet connexion)? I mean is it possible to use local account temporarily, just during broken internet period?
Yes. I believe that it is possible to move between local and online accounts, as long as you have access to a copy of the key file whilst you are offline.