Although I am not sure why you'd want to just have one or two litters and there's the question of these guys being pedigreed or quality, or even having a known background to prevent genetic issues (perhaps this is in another thread), I will answer your question.
Yes you can get him neutered after you have a couple of litters assuming they even breed in the first place and that you can successfully reintroduce them after the first and or second litter. First questions are you willing to risk losing the female and incurring expensive c-section bills, and the second is are you willing to risk anesthesia for the male to have the surgery? Small animals like chinchillas are at higher risk for complications from anesthesia like never waking up, going off their feed resulting in hand feeding and possibly stasis. Sometimes these things happen, so best to think about them now.
Second, yes he will likely try to mount her because she will still be going into heat each month. He won't know he's neutered. She could become very agitated by this and become very aggressive towards him resulting in mildly slipped fur to even the point of attacking him and killing him. Not uncommon. This is why most breeders breed in a run set up to allow males an escape route to safety. This may happen BEFORE he's neutered when you are trying for these litters as well.
Third, yes there are chances if you put him back with her before all the sperm have a chance to die in the tract. You'd need a separate cage set up for him to recover in for several weeks post surgery.
You need to separate the male as soon as you can confirm pregnancy - 9 times out of 10 you will wake up one day and the babies will just be there and if he's in there breed back has most likely already occurred.