now they are in the system they’ll need the standard documents. But this bloke is a bit of a special case. Overseas born Thai citizens can’t get on the house registration immediately like locally born kids so embassies can bypass the need to be in the house registration for an overseas born Thais first passport
You need to get your first thai passport back in the UK. Without an ID card you can’t apply for a passport here in Thailand. Embassies can generally issue your first passport without an ID card
Simple answer is yes. Enrolled in a school with the proper credentials, documents supplied by the school, 500k per child in the bank and an extension is possible.