I have had bantams that were crowing and mounting by that age. I've had some do it by 8 weeks (not quite 2 months).Yes, I understand that but at 3 months of age, most roosters (at least afaIk) are not yet crowing & mounting.
I am actually currently talking to a vet that is willing to caponize a rooster for me but in order to not blotch the surgery, the testes need to be developed further so they are more easily identifiable/removable. I should also mention that I am talking about a bantam breed in my case...
As a general rule of thumb, small chickens mature sooner than big chickens. So bantams often reach sexual maturity sooner than larger chickens. Of course there are exceptions, so I cannot be sure when YOUR cockerel will start doing these things. But I would not count on him waiting 3+ months.