To answer your questions - you don't have to inform him of the birth. Although probably a basic courtesy to tell him, once you & baby are home. Put in your CMS claim as soon as you are home from hospital.
You don't need a solicitor (yet).
When the baby is born, register little one with your surname. You cannot add ex's name to the birth certificate unless he is physically present.
He can then apply to the court to be added as father. You could accept his request or you could dispute it and require a dna test. If the baby is his, this serves only to slow the process down. Until he is awarded parental responsibility by the courts, he has no rights.
As far as access is concerned, until he has pr, he has no right of access. However, your child has a right to a relationship with their father so think carefully about what will work for you.
Something like an hour or two, every other day, at your home to begin with. Gradually increasing that as he and the baby develop a bond and he learns how to care for a baby - food, nappies, sleep routine etc. Obviously any access has to allow for you to breast feed.
You have 18 years to co-parent so ideally you come to a calm and amicable agreement on access. But if he insists on trying to bully & threaten you, you can use the court process to slow down access until baby is a few months old.
If he gave you a crib, you don't need to give it back. Baby won't be over-nighting at his for at least a year so he is being ridiculous.
Generally though, be reasonable, accept that your babe is entitled to know his/her dad, aim for a mutually supportive relationship. You are in this for the long haul and your child's life will be happier if the two of you can find a way to share calmly. Don't put up with bullying though. Keep all communications that are threatening in tone.
Congratulations & good luck xx