Immigrationboards.com

1. Apply British Passport from Overseas - £100+ && 12 months (max) Yes, it takes long so probably not the best route if you want them to return to the UK quickly

2. Apply Indian Passport + Right of Abode - £500 && 4 months (max) This is probably your only and best option.
(a) This appears to be the cheaper (cost wise) / faster (time wise) of all options - is this understanding correct?
(b) We are very nervous of the rejections in this category with no appeals whatsoever. Child is British by descent, there should not be any issues.

3. Apply Indian Passport + Visit Visa for Child A British citizen can't apply for an entry clearance visa. This option unlikely to work (genuine visitor test).
(a) Can this route be suggested assuming the child would apply for british passport on arrival in UK?

4. Apply Indian Passport + "Child or Dependant of a Settled Person - £1000 + 3 months (max) Very expensive and also, British citizens can't apply for entry clearance as they already have right of abode.
(a) Is this even suggested for our case

5. Apply Indian Passport + "Family member of an EEA national " Not applicable. You are not considered and EEA person in your country of nationality. So as British, you are only British and not an EEA/EU citizen.
(a) the fee tracker website suggest this as a free of charge visa?

(a) This appears to be the cheaper (cost wise) / faster (time wise) of all options - is this understanding correct?
(b) We are very nervous of the rejections in this category with no appeals whatsoever.

3. Apply Indian Passport + Visit Visa for Child
(a) Can this route be suggested assuming the child would apply for british passport on arrival in UK?

4. Apply Indian Passport + "Child or Dependant of a Settled Person - £1000 + 3 months (max)
(a) Is this even suggested for our case

5. Apply Indian Passport + "Family member of an EEA national "
(a) the fee tracker website suggest this as a free of charge visa?