I'm only just now finding out about NI credits, I knew nothing about them. I've been a SAHM for many years.
Gosh OP this is a mess. Never mind, better late than never. For at least some of the time you were claiming child benefit (as long as it was being paid to your name not his) you will have (automatically I think) been credited with NI payments.
You can ask for a pension forecast. This will tell you how many years NI you need for a full state pension and how many you currently have. If you're planning to work until retirement age you can work out how many years of contributions you'll be making. If you're not going to have enough years you can see if you're able to pay voluntary contributions for any years you've missed and which you haven't received automatic NI credits for.
None of this is important right now though. What's most important is the divorce and especially severing joint finances. So focus on this.
Family don't have to fund your divorce entirely, you're going to get a job and by the looks of it have some UC too. Half is better than the "none" you thought you'd get. Ask them to fund the first few meetings with a solicitor though, if they want to help. It will get the ball rolling.
Apply for council tax reduction on the grounds of low income, this is a separate claim to UC and also separate to other discount I'm about to mention. As far as I know it's not backdated, so get onto it ASAP. Do your adult children live with you? If they do, you won't be able to claim 25% single-adult-occupancy discount.
As soon as he pays into the joint account so the overdraft is cleared, get it closed/frozen/you removed. This is absolutely vital. You don't need to live off the overdraft, you'll have UC as well as child maintenance. Keeping this joint account going is shooting yourself in the foot and helping destroy your future.
Use a food bank (school or GP can refer, as can multiple other official organisations/people so ask whoever you have available). Find where community pantry is for your area (cheap food). Take out a credit card in your own name. Borrow from family. Ask UC for an advanced payment. Ask jobcentre for a Crisis Loan (which you should easily get, with zero income). Ask your utility providers about specific schemes for people on a low income and get those. Change all your utility bills to quarterly billing to give yourself 3 months of zero payments, to give you a chance to get alternative finances set up, you can go back to direct debits later if you prefer it. Use your supermarket loyalty points to pay for your shopping. Do anything and everything other than relying on this joint account overdraft.
If for some reason you can't get the joint account closed/frozen/yourself removed - play smart. Ask him, since he's happy for you to solely use the joint account, to get himself removed from it. Just that. That won't stop him from being able to pay into it (for child maintenance or whatever else he's planning to pay in there, (you can just go along with that for now)). He can tell his bank to do a bank transfer into any account he likes. He doesn't need login details or password etc, only account number, name, and sort code. I say this in case he uses it as an argument for why he "can't" remove himself.
Agree/be non-committal whatever he says about direct debits/debts etc (nothing in writing!). Then, after the joint account is solely yours, tell him you're cancelling all the direct debits that aren't yours ie all those debts in his name etc. There's nothing he can do about it if he's not part of the account. Also you can tell your bank not to accept payments from his bank, if he's trying to put other money in there for you to pay his bills with etc and get child maintenance collected by CMS from his wages instead. But I don't think it'll come to this, banks must deal with divorcing couples all the time. I'm sure getting the account frozen, at least, will be easy enough.