Can (or can not) an Auxiliarist wear the frame cover (hat) if he does not have any "rank" and is a new member?

All Auxiliary members can wear a Combination Cover.  Those with positions of DCDR /DVC (wear a Silver Oak leaf and Eagles) and higher wear Acorns and Oak leafs on the visor (equivalent of CDR; CAPT).  Commodores wear a double set (equivalent of Admirals).

See the AUXMAN for more details.