Oh OP I'm so sorry, that is so wearing ☹️
Your DH is ridiculous, I'm sorry. Mine WFH but 2.5 jobs, does all the cooking for us (well did for ages, I'd try and help make a main dish for dinner in the daytime sometimes and do all the food for our DS but DH always makes us dinner), does the large majority of the cleaning. Did all of it for ages! He's so busy but he'll take DS while I finish making his food if he's really fussy and I'm struggling.
Mine is breastfed so at 13 months has only recently started doing what could be considered sleeping through the night, then started teething again and stopped. This only happened at all because DH started settling him at night instead of me. We realised he could go all day without milk from me when I went back to work and on his nursery days they were able to get him to sleep without milk or a pram.
Mine was in the next to me for ages tbh. I used to hold him for 20 min then transfer him to the next to me and his first stretch of the night would be the longest. After 4 months he'd wake up every 2h at least.
At 6 months he stopped going down in it at all for about a month, he would wake up as soon as he was transferred regardless of what I did. Solid bedtime routine since 3 months as well. Really annoying having a friend ask if I'd considered using a sleep sack to help him realise it was bedtime (yes, he's always had one and he knows!). I ended up resorting to putting him in the next to me and bending over it to breastfeed him in it on his back so he stayed asleep in it - ridiculous but I was desperate for some time on my own and I'd also had him round the clock for about 3 months straight.
Even now he's in the big crib, he still feeds to sleep and I often get in it with him to transfer him, sometimes he'll wake up a bit and feed more, then I can roll away from him and he'll do a good solid stretch, then DH will settle him if he wakes up. Since DH started this, we've seen DS on the monitor able to wake up, sit up, look around and go back to sleep.
I say that to say, sorry for previously saying I wouldn't watch TV while mine was in the playpen - I wouldn't but have a supportive DH and some time in the evening while baby is asleep. I would be saying to your DH either take on cooking duties or getting baby settled in her crib/night wakes. He's not being a partner at all, that is beyond crap. Breaks from work while you do literally everything for the baby and the three of you at home, then calling YOU lazy! I'd actually be outraged.
Oh and I was extremely precious about my DS's food and did all of it from scratch myself, low sodium everything apart from the odd bit of meat my DH would make him as I don't eat it myself and don't trust myself to prep it properly. Buttered toast is absolutely fine and your DH can sod off! I don't agree that dads should get no say in parenting decisions/care for their kids if they're not doing the main care of them but yours is slacking so much and is just ridiculous about the food as well. I'd go on strike if I was you, OP!