You’re missing the point that if you apply for a Non O visa based on being over 50 from the UK you don’t need insurance - nor the medical certificate and police check.
Depends on your child’s passport. If their nationality requires a visa then they need their own to enter Thailand. It’s irrelevant what visa you may hold.
Phuket requires a new TM30 filed even if you stay one night in a hotel or hospital in country (as well as every time you return to Thailand). They do at least have the drive up window so it doesn’t take too long in most cases.