help needed - baby's passport application

Part A)
I got my naturalisation certificate recently. I am about to apply for passport.
My understanding is that I need to attach with my application:
1) My current passport
2) Naturalisation certificate.

Question: is my understanding right?

Part B)
I have a new born baby having no passport. I have the birth certificate. I want to apply for his passport. My understanding is that I need to send my naturalisation certificate with baby's application to prove baby's eligibility for the passport. Am I right?

So my naturalisation certificate is needed for both my passport aplication and baby's application.

Question:
1) Can I send my application + Baby's application - in the same envelop to cover both application erquirements?

You will certainly need you nat cert for both, I think you can send it in one envelope. Why don't you ask the local post office when you go to pick up the passport application forms, they will know it for sure.

If your baby was born before you received your naturalisation certificate, then you need to prove that you were holding ILR/PR at the time of baby's birth. In any case, you can send a joint family passport application where relevant documents are shared among applicants.