Yes, the cat will calm down after neutering.  It may take several weeks for
all the hormones to work out of his system.
You may want to spend some time educating the boyfriend's son on how to
handle cats.  He should not have tried to take away a toy while the cat was
all riled up.

He will calm down after getting neutered. It takes a few weeks for the
hormones to dissipate. The running outside is most likely a hormone issue.
Mounting his brother is probably mostly a dominance issue and may not settle
a whole lot. He may always show his dominance that way. It's normal and fine
as long as no cat is coming away bloody.

That said, there are some serious issues here with how to handle and treat
cats. Cats are animals. They are not robots. They are not toys. They get
pissed when handled a certain way. They have emotions and feelings and moods.

Some cats are more tolerant than others. And, after "hours" of playing, the
cat was probably either really tired of being bothered or very worked up.

Generally speaking, if your cat bites when you do something, DON'T DO THAT.
If you know one of them is dominant and gets riled, don't play rough with
him. EVER. How you play with him teaches him how to interact with you.
He is a cat. He has fur and thick skin. When he bites another cat, it won't
hurt the other cat as much as it would hurt you. He doesn't know that. He's
just a cat.

You don't _grab_ a cat when he's riled and expect to not at least get nipped.
Will ALL cats nip? Certainly not. But don't expect that yours won't. Some
cats are mellow. Some aren't.

And keep in mind that if the cat really wanted to hurt (attack) the son, he'd
be in the hospital, badly injured, with stitches. I've seen a cat honestly
attack a human. It wasn't pretty.
The cat was either playing rough or just giving a warning. Teach the son how
to interact with the cat and teach the cat to respect human flesh. Respect is
a two-way street.