I don't know about child passports but for adults you can renew up to 10 years after expiry. Longer than 10 years you have to complete the full process, as if it was your 1st passport.
Sent mine a week ago using Thailand Post air mail (tracked) at 250 baht. I was told it could take about 3 weeks, which is no problem.
If you send EMS (tracked) it will cost around 1,000 baht and take about 1 week.
You can renew 8 months early, but you will lose those months. UK passports now commence from the date of issue. Previously you could apply early and get 10 years from the expiry date of the old passport (I think it was up to 6 months added on).
Changes made due to Brexit.
https://www.nookiesdelights.3baht.net/location.htm
He does arrange delivery by courier or, if you're lucky you may be on one of his regular routes. Talk to Paul, his phone number is on the website.