Can i used different Database on remote server for civicrm logging?
Yes perfectly possible, we do it all the time. You can set the logging DSN in your settings file (CIVICRM_LOGGING_DSN) if its not set then CiviCRM falls back to the CIVICRM_DSN
Sorry - just read your whole question!
I would check that the user has permissions from the CIVICRM_DSN to the CIVICRM_LOGGING_DSN i.e. if the CiviCRM database user cannot access the logging database then maybe thats causing the issue.