The order numbers are the references of the Part 2 Order (an administrative piece of paper)in his unit on which the entry was recorded. Thus the first one was Part 2 Order number 65 of 1942 by the unit concerned, they can safely be ignored!
He moves from the training battalion to 556 Company in March 43.
The S is the start of the word Serial. Serial RGXGA is the draft recognition code (the letters don't mean anything) identifying the draft (a large body of men posted overseas) in this case. He was SOS, Struck off Strength, removed from the books if you like, of 2 DBRE in 15 Jun 43 to join the draft on 16 Jun 43 for N Africa.
Redesignated is the common term for a change of title of the unit he is in.
The information I gave in your earlier thread in January which you don't seem to have replied to, it seemed that 66 Field Coy remained in the Middle East. Can we see the remainder of the postings record.
MaxD