Visa exempt entry* and yes, that's your best option. 60 day covid unable to travel extension are still available until November 26th, so if you applied for that after you entered you'd have the same 90 days (if your plan was to extend the TV 30 days) that your family would have.
No, don't have to post anything it's all electronic now.
I mean you can apply for the TP if you're entering visa exempt. If you have a visa it asks for the visa number, guess it wouldn't matter if you applied visa exempt and just arrived with a visa.
As of Oct 1st, visas are now issued digitally. Go to the Thai embassies website in the UK and apply online. Should take a few days, they'll email you the visa. Print it out and take the paper with you.
You also will need to apply for the Thailand pass after you get the visa.