Buns mature at around 4-5 months, depending on the breed, the bigger the bun the slower they are to mature. He is defiently old enough to be neutered, so have a look for an experienced vet who will do them both. Females should be spayed as it prevents womb cancer and other reproductive cancers that occurs in bascially all females aged 4 or older, sometimes sooner though, and once they get it, and by the time you have noticed it, poor bun will have to be put to sleep as it spreads very quickly as its agressive!
It also will make her calmer, happier (no mad hormones) and will prevent any accidental pregnancies.
If you want to bond the two, she'll have to be spayed anyway otherwise he'll probably hump her all the time even after being neutered!
If you get them done at the same time you only need to wait until they have healed before you can bond them!
I'd also ask the vet to cut off those rings as unless you are serious in showing, they are totally unneccessary.
Just a quick question, but when you say two teir hutch, what size is each teir? Buns need a hutch and a run, especially bigger buns like yours.
Minimum should be 6ft x 4ft x 4ft with a nice big secure run so as they can binky and stretch.