Sorry, I saw this yesterday, but was at work, and then forgot to reply later.
Am I correct in thinking the total cost for my (7year old) son and I to extend our visas from within the UK will be £4,066? £1,033 per visa and £1,000 per IHS? Are there any other costs I’m missing other than cost of ink to print stuff out? Do they charge for the enrolment of biometrics?
You have:
£1033 visa fee each
£1000 IHS each
so, yes, that's £4066 in total for the visa costs.
There are also other optional costs for appointments to give your biometrics and submit the application, such as an appointment on certain days/times, as a premium appointment for £800 per application to get a 24-hour decision, appointments where they scan your documents for you etc.
I'm not sure about biometrics cost, since they have a new application system now, so I'm not sure if you need to pay the £19.20 to give biometrics or not.
Another question is that my son’s passport expires 1 August 2021 (we apply for FLR feb 2020), am I wrong to think that it needs to be renewed before we apply to extend? I’m so confused on the process of how to renew his passport anyway. Because he’s a minor, do we need to go to the US embassy in London by appointment?
No, you can extend the visa before you renew his passport, as the visa will be issued as a BRP card anyway. So, you can apply for FLR(M) in Feb 2020, and then renew his passport in 2021.
Not sure how you apply for the passport if he is a minor - you'll need to check the US Embassy website:
https://uk.usembassy.gov/u-s-citizen-services/u-s-passports/child-passport-renewal-under-age-of-16/Looks like you will need to go in person to renew his passport if he is under 16.