I'm sorry this has happened.
You need to tey and source a car seat from somewhere or someone else urgently. You could try Facebook marketplace, putting a request out on social media, freecycle, specialist baby and child charity shops etc
As others have said he doesnt have automatic rights for 50 50 care as building up to that gradually is in the childs best interests. Presumably if youd been together you would have been taking maternity leave so you would have been the primary caregiver.
In all your discussions going forward make sure you reference 'the baby's best interests' rather than what you need or your preferences.
So state that you are keen to support working up to 50 50 care eventually as you know that for older children, having a strong bond with the father is important and will do your best to facilitate this. Find some studies or court decisions that evidence the best way to achieve this is little and often (eg estranged fathers rarely have younger babies overnight). Put forward a schedule of contact that is frequent but short, initially with you, then at your house, then him taking the baby out for a few hours. Personally I'd persevere with breastfeeding if you can if you are worried he is not going to be reasonable and is going to insist on taking the baby away for extended periods of time.
The birth is all about the health of the mother, you dont need to tell him anything until afterwards. And I'd wait and see when that afterwards is (eg he has no 'rights' to come and visit in hospital - you are there for YOUR medical procedure and are entitled to privacy and most people wouldnt want an ex to see them with boobs out, and vulnerable etc.
Register the birth without him and choose whatever name and make sure your surname is given. You will be the primary carer and registering for everything and it will be a pain if you have a different name.
Best of luck. It sounds like he wont make things easy so I'd advise waiting before responding to him, gritting your teeth and appearing reasonable, always referencing the babys interests, and keeping everything in writing so that if or when it goes to court you can demonstrate that you've not been unreasonable and not refused contact