I have a quick question hopefully quick ..

My son who is 2 years old was born in Uk and once I got my ILR we applied for his British citizenship via MN1 form.
We received his British citizenship letter and we wanted to know next steps. I know we can apply for British passport but my question is regarding certificate of entitlement.
1. Is my son eligible to apply for certificate of entitlement
2. Can we travel to India (original passport) and get back to UK with naturalisation letter or we need a British passport / COE?
3. We need to travel in December for family reasons so can we go to India and apply for UK visitor visa for my son and get back and apply for COe ?
I know we need to pay more and the time is also around 6 months for COE but wanted to check how best we proceed.
Thanks in advance for your support