I'm not totally sure about the HMs attached to the Fleet Marine Force (FMF). I know they are authorized to wear the Marine MARPAT uniform, and they can earn a special qualification while attached to the FMF. Now, I don't know this for a FACT, but I would assume that HMs are issued rifles alongside the other Marines. Once again, just my assumption.
As far as the "Carrier field" - there's isn't a field in the Navy that is totally dedicated to being on carriers. What else were you thinking of doing?