Does AA Gold have any status on Gulf Air?
 

Specifically can I request exit row seat and use the business class check in?

Unfortunately, AFAIK, as Gulf Air is not part of the oneworld alliance, without any special arrangements such as those AA and AS have there is no reciprocity or status recognition between Gulf Air and American Airlines. As well, at this point, unless you are flying on an AA codeshare on Gulf Air you will only earn redeemable, not Elite-Qualifying, miles.