... you can buy at the immigration office or at the airport before you depart. It only takes about 15 minutes and you get it before you stamp out through immigration. If you do a group search "re-entry permit" you will get all the info you need.
... I had the 1 year multi entry for a few years but I was travelling out and in a lot for work so the 90 day max wasn't an issue. Since the end of 2020 I've had the 1 year extensions after my initial 90 day non O visa and just get a re-entry permit if I'm travelling now.
Reading between the lines, it seems you picked the wrong visa. A non O 90 day single entry would have been better as you don't have to leave the country. Just get a 1 year extension before the 90 days finish then you are good to stay for 1 year without leaving. The 1 year extension can be renewed every year indefinitely providing you meet the requirements. If you need to leave you simply get a single or multiple re-entry permit before you leave which allows you to keep your extension alive.
... VFS are very efficient, I've used them in Chiang Mai, Bangkok and Saigon for 7 PP applications and 3 visa applications and I've had no issues at all ... Covid aside, when it took 3 months for my kids PP's to arrive, although that was expected.
... yes probably. Apply through VFS Global, you keep your old PP and the new one is back in 2 weeks. I've done it several times over the years for me and my kids. That said, a same day turnaround at the passport office in UK should be ok.
Visa exempt stamps and extensions are void as soon as you exit the country so you would simply get another 60 day free visa exempt stamp when you re-enter, which of course can be extended by a further 30 days at the IO for 1900 baht.
... AFAIK, there is no rule on this and it really is in the hands of the individual IO who stamps you in. In fact I have seen many posts regarding the opposite, where the IO stamped the person in for 30 days on visa exempt when they had the visa but the IO didn't see it. In those cases the visa holder had to exit and re-enter on their 90 day non O. My guess if you ask the IO will say cannot but if you don't ask the IO may not see the visa and give a 30 day stamp. Unfortunately TiT where rules are very often made up to suit the mood of the official you're dealing with. 🤷♂️