Yes, completely IGNORE anything that comes from him! If you want, call the police, as he's breaching the court order (AGAIN) and is not to be contacting you. It would be a good idea to keep them apprised of his behaviours and his breaches. But that's obviously up to you as you're... what's the technical term here? Oh yes, A BIT BLOODY BUSY!!
As for the solicitors, as important as their work may be, you've got time still (iirc), so I'd be tempted to send a quick, possibly terse, "I've just given birth mere days ago and have my hands just a bit full atm. Could you give me a few days, please ffs?' and then leave it at that for as long as you need.
Oh Lolli, how I wish this would all just go away for you love. I wish I could take it off you, or help somehow. It's so fucking unfair. But you are doing fine. You are doing wonderfully!
It may not look like you've got much now, but look what you're up against! Look what you're battling through! Look what you've just escaped from! You are doing AWESOMELY when you look at all of it in one picture!
My family (Mum and DS&DBs) were DIRT POOR when I was a kid, and I had no clue. I can't adequately explain to you how poor. All of us had to live with my DGP and my youngest uncle for years. Then we also lived in a caravan with anywhere between SEVEN AND TEN PEOPLE (depending on the day) for several years, and I never once thought that maybe we didn't have anything, not until I was a teenager! Young kids don't know nor care that their seat is borrowed, that they're on a travel cot and not some expensive silken basket, that their onesies came down from their older DB, or any of that. And being told 'no, you can't have and don't need that useless expensive thing' is indeed character building! :) It's not just a cliche! It's made me a very frugal, very practical person. So don't worry about that stuff for them.
You love your kids fiercely and they love you, and that is literally all that matters. For the first years, all that DC need is the very basics - food, somewhere warm to sleep, four walls - and Mummy's love, and you've got more than enough of that! Anything else can be improvised. They don't need the fanciest gadgets, they don't need expensive toys (they always prefer the bloody box it came in anyhow!), they don't need special nappies or organic strawberries or 'smart' technology. Of course having a bit more makes things easier, but I assure you, your DC will be perfectly happy and fulfilled just as you are. And you WILL get through this and move on.
Please, if there is every anything we can do, please just tell us. And as always, we are here for you. 
Cuddles to the beautiful new boy and the other DC from the internet!
And... I know it's a bit early for this, but might I suggest... I've been thinking, once you're finished with all this mess and all of the legal things are settled, you may want to look into working for some kind of specialist solicitor or a women's shelter / legal aid company! Maybe even start your own, a company to help women and mums navigate the legal world of leaving an abusive DP or perhaps oversee or keep on solicitors? You've learned so much, and done soooo much of this all on your own, it seems you've got quite the knack for it! You're a right natural!