Wrong. See links above. Children have to apply in person. Once the Embassy opens for normal activity, they will be able to renew in Thailand. Impossible. They either got an emergency passport issued within 3 days or they waited at least 7 weeks. See links above It's a whole new Covid kind of world. See links above.
The current delay in renewing adult US passports is about 6 weeks. https://www.passportwaitingtime.com/ You cannot renew your child's passport by mail and because of the Covid shutdown and backlog of unprocessed renewals, in person passport processing is currently limited to "life and death" processing only. https://travel.state.gov/content/travel/en/traveladvisories/ea/passport-covid-19.html https://travel.state.gov/content/travel/en/passports/need-passport/under-16.html