I'm sure you are dealing with tremendous amounts of shock and fear right now. I could give you lots of suggestions for proceeding, but I'm concerned that it could be overwhelming.
I think you need to focus on the basics:
1. Do not make any decisions when you are overwhelmed, afraid, numb, etc.
2. Do not give a bully (and that is how he is behaving) the satisfaction of fearing his threats. He may chicken out in telling the children, the children likely suspect something has been brewing and will at some level be better with it in the open, or if he does tell them and does so in a rushed manner as he is threatening, the kids will see the mess going on there. You are their rock. Forget what he says and how. It is you they will respond to. If you take away the leverage he has in your fear of telling the children, then his threats are nothing.
3. Do not fear being served. If there is shame or humiliation attached, it belongs solely to him.
4. Whatever is motivating this rapid cycling and demands will wane relatively quickly if not satisfied.
5. Do NOTHING without talking to your own lawyer. Find a specialist in family law (look on the American College of Matrimonial Lawyers website) or contact the state bar for your state and ask if they have a certification program for family law attorneys. You do not want someone who also does criminal, civil, etc. You want someone not too young or too old. Not too experienced (pricey) or too inexperienced. At least 5 years in the practice area. Find someone from a small to mid-size firm. You don't want a situation where you have a partner supervising a newbie. You'll have the high biller and the work will be done by the newbie.
Ask who will do the work on your case and make sure you meet them and like them. Find someone who believes in attempting to resolve cases out of court, but is prepared to go to trial if that is not possible. You don't want someone "out for blood" that will push you to litigate everything.
Please secure the assets (as in transferring your part of joint funds) and then move at your pace. In my state a contested divorce lasts 1-2 years. A lot can happen in that time. A red, hot burning affair will generally burn out before then.
It may not be possible right now, but think about what you want. Do you want the divorce now? Do you not know and want to buy time while you make up your mind? Are you prepared to endure several years of a heavy replay? If you know you want a divorce and won't change your mind, move forward with all alacrity. If you aren't sure, hire an attorney you like and trust and let him do the heavy lifting on his divorce while you give yourself time and distance to make the best decisions for you and the boys (because he just can't do that right now).
I know it is scary, but it is going to be OK. You DO NOT have to do this at his pace.
If he tells the boys, he tells them. But do not allow this to be a source of bullying. Contact the school and talk to the guidance counselor and express some concern about the exams and whether he can take them later or everyone can assess his situation before that decision is made.
What grade is the oldest son in? If it is 8th grade, then honestly the grades don't even matter. Better he should know and start getting through the processing. My S had a horrible year last year for 8th, but has pulled it back together for 9th.
You have to take the time now. When anyone forces you into a pressure sell, you know you are getting a bad deal. If nothing else, why help him with the OW and whatever it is that is motivating the need for speed.
