As others have said this is abusive. Honestly each of your messages piled more and more evidence onto that fact. He's gas lighting you and his mum's enabling it. Your mum is on your side and sees through him but not necessarily in the most helpful way for you.
The HV saw his coercive and controlling behaviour and wanted to check you were OK. Why does he think HV's don't help dads? He didn't express any desire for help but you're clearly struggling post birth. Of course she should focus on you not him! He IS a man baby if he wants his life exactly as it was before he became a dad. Life doesn't work like that! And yes, for now his needs come last. Baby first, then mum, then dad.
You're the main care giver. Parenting a baby is a full time job! It's not a holiday! Going to baby groups is supportive from people who are in the same situation. Men don't see how hard it is until they face the relentlessness for weeks on end.
My DH is very tidy and was pissy when he came home to a messy house. I did as much as I could but it was relentless like the caring I was also doing. He was between jobs for a couple of months so I went back to work early. After just a couple of weeks he apologised and said he understood why it wasn't possible to do everything around the house AND care for a baby. I don't suggest you give that level of responsibility to your man baby but childcare is not as easy as you're making it look!
I would think long and hard and talk to your mum when she visits to understand if there's any future in your relationship. Me, I'd bin him off. You've already got one baby, you don't need another.
And his mum only making him single portion dinners? She can get in the bin as well! What an awful thing to do when you are full-time caring for her grandchild!