There is no legal requirement for an IDP (at least not if you have a UK licence written in English). Obviously, you need a valid licence for the class of vehicle you intend to use but it's always amused me how people that have never been on a motorbike in their lives and have no licence as such, all of a sudden think they are entitled and able to ride a mototbike simply because they are in Thailand.
If you're already in Thailand and not started to claim yet you probably won't be able to connect to the UK Pension website to start the claim. It may work using a VPN but I don't know enough about them. That means you will have to use their "claim from overeas" portal and as the first response stated, that means you will not get any annual increases.
I always go to immigration whenever I get back. Show them I was out of the country when the 90 lapsed and when I was stamped back into the country so I have a 90 day report date always attached to the passport but yes, the new date always runs from the date of re-entry.
That is to say, I had one month insurance for my TP application but my return ticket far exceeded that. If you're already here, nobody will even look at it when you exit.
That happened to me just a couple of days ago. Below the box you are trying to complete is another, asking if you want to submit further info. Use that box and the date option should work. Simply fill all the details into the second box then cut and paste into the "proper" place. Then delete the info in the second box. Good to go!!