My grace period ended last year. If I go back to the old univ, will the OPT authorization go through USCIS or only via the international officer (Cap=Gap rule)?
-Do you mean your OPT expired last year? If so, you are not qualifed for the Cap-Gap rule benefit to extend your F1 any more. So, you do not need to bother your old school when you graduated from.
Last, I have one short-term employment (2-month). Will that be considered as immoral?
-No.