Ok. If you aren't married daddy doesn't have any legal rights. He can't just take off with baby.
Baby shouldn't be w/o mom for more than an hour or 2 as a newborn. Nipple confusion is real and "just pumping" isn't as easy or convenient as it sounds. Offering a bottle w/i the first few weeks can lead to unnecessary problems (not to say that if baby must have a bottle, for some reason, it's the end of the world) so it should be avoided.
It sounds like you are going to have to have a talk with dad about what will realistically be happening when baby is born. Dad can have plenty of bonding time with baby, with you around too.
Because you are not married, he has no right to be in your room when you give birth, or to visit after baby is born. YOU control who has access to your newborn.
And as others have said, pumping and bottle feeding in the early days/weeks is fraught with problems. If you choose to involve him in parenting, he won't have the baby without you present for quite some time.
Unfortunately your ex is underestimating both the challenges of breastfeeding as well as the ease of providing pumped milk for an infant. If exclusively breastfeeding is important to you, the baby should ideally not have bottles for the first month of her life, as bottle-feeding can dissuade some babies from latching. Also, some mothers do not respond well to a breast pump, and there's no way of knowing whether you will or not until you actually have to do it.
I think you're going to have to inform your ex that you're not going to be able to commit to any custody agreement before the baby is born, and that you can't promise that you'll be able to let her be taken for unsupervised visits while she's still very young. If your ex decides to get ugly about it and take you to court, judges do tend to recognize the unique needs of exclusively breastfeeding infants in the first few months of life. You should seek counsel from a family law attorney ASAP to see if there are any custody laws specifically related to breastfed infants in your state, but even if there are not you are very likely to be given primary custody of your baby for the first year or so of her life.
If you weren't breastfeeding, there would be absolutely no problem with him parenting a newborn child equally with you. It is good for baby to bond with both parents. Mom needn't be the only caretaker.
But you are breastfeeding, and I agree completely with what the previous poster says about that.
Dad needs to learn about breastfeeding. It would be a good idea to point him toward any educational material that you've read to prepare for breastfeeding, so the two of you can have an equal understanding of what is involved.
Pippin and LizB are correct.
At the hospital, you as a patient have 100% the right to say who can go in your room. The nurses can help manage who goes in your room. Tell them who is allowed when you do go to the hospital. That said - it may be nice to have him there. If you do not want him in the room, that is OK. He can stay out in the hall until the baby arrives. And then he can see his child after you nurse (best to nurse right after delivery)
As for visitation, the two of you need to come up with a plan. In the early weeks, its best for baby to settle in one place. Arrange times he can come to visit. Avoid bottles and that pump at least for the first month or two.
It is not suggested to pump at the beginning. You should wait until your supply has come in and normalized, which occurs around 8-12 weeks. When a baby is first born, they will want/need to breastfeed very often. Your newborn will want to feed every 30-90 minutes at the start. And yes, giving bottles (especially right away) can cause latching issues.
He is going to need to wait a couple months before he can have overnights. By 8+ weeks you can start pumping and sending frozen breastmilk for him to feed the baby. In the meantime, you should allow him to spend time with his child during the day. I suggest buying a good quality pump, like a Medela Pumping in Style, as well as some breastmilk storage bags.
Courts DO try to have BOTH parents parenting. Ideally they would like 50/50 arrangements. Babies do not only need mothers as caregivers, or one single caregiver. The bond with dad is equally as important as the bond with mom. Breastfeeding can slightly change the situation, and they may make extra arrangements to allow you to breastfeed.
First of all, no judge is going to give him more than a couple hours of visitation with a newborn so you don't have to worry about that as long as you aren't a drug addict.
Just breast feed the baby and move on. It makes NO difference what the father wants - only what is best for the baby.