He really does sound like a typical narc. He lives to get his ego fed and wants to project the image of the perfect father without actually putting in the hard work of parenting. He even expects your DD to feed his ego (can't cope with her crying, expects her to behave perfectly at all times, to give him nothing but affection). Meanwhile he is incapable of giving any her any real emotional support or affection. They are really just empty hollow souls who suck emotional energy from anyone who they come across. The more you learn about what motivates narcissists, the better equipped you will become at handling his behaviour when you have to coparent. The best method is grey rock. Do not give him any sort of emotional reaction as this is what he feeds off.
His dislike of you breastfeeding is probably because he is jealous of you giving your attention to anyone but him (and yes that includes your DD). I suspect that's why he wants to send her to nursery, so he can have you to himself or at least know you are not bonding with her when you are together. Please dont listen to what he wants as everything he says is for his own agenda and not your DDs.
It's really difficult for you OP because alot of this is impossible to prove to the court system, so you may struggle to demand supervised contact only. I certainly would try and limit any time he has her on his own as he has already shown you he is incapable of putting her needs first. Also, just her witnessing the emotional abuse towards you will alter how her tiny brain develops (studies have shown this) and she may be very likely to seek out abusive men when she is older if he is able to have unlimited access to her.
In some ways it is easier for me as my exH was also physically abusive to me so it was easier to 'prove' abuse, plus he is also in prison now so I have managed to cut contact completely. My children have all been left with emotional problems though due to the abuse they witnessed to me and also what he inflicted in them. Emotional abuse can be just as damaging and harder to recover from than physical so I am glad you are finally recognising this for what he is.
Does he show any coercive behaviours that would fit under the new coercive control laws? If so, gather as much evidence as you can.
Men like this become particularly nasty over child contact arrangements (it's about control and not about them wanting to see their child). They will tell outright lies about you to anyone who will listen to make you appear as a bad parent or that you are maliciously stopping contact (smear campaign) and trust me, when they know there is no chance you will take them back, there are no limits to how low they will go. Prepare yourself for this because when you kick him out he will be plotting his revenge and you need to stay 2 steps ahead at all times. Unfortunately the courts rarely recognise this type of abuse and will give men like this many many chances. I've seen it happen way too often.