Yes of course a scooter is a motorcycle.

Yes you can drive a car with a foreign car licence. But not a motorcycle unless you have a foreign motorcycle licence.

People, if he only has a car licence at home, that's all he has here with an IDP. It's not a magic document. He can't legally drive a motorcycle here. Maybe can con some police who can't read English on the IDP but it's illegal. In Thailand there is no 50cc exemption for car licence holders.

The immigration people at Hua Hin are very good. You will have no problem getting an extension there if you follow the fairly simple requirements. They have a spot to pick up the relevant forms and a knowledgeable photocopy lady that prepares the required copies of everything and bundles them up. It usually takes less than an hour in and out after that in the queue. You should have no problem. Your GP will know you don't have the conditions listed for the medical, assuming you have been going to him for some time and will not need to actually test anything. The diseases listed are pretty exotic!!

I don't think so.

Not needed in Hua Hin. YMMV.

If you go late, you could get deported. You'll be in the country illegally. Unlikely but a possibility.

What about getting an O-A for yourself. You are over 50 so should qualify. I believe your wife can be under 50 if she applies with you at your countries embassy. Check your countries Thai embassy Web site. This will give you a 1 year ME. No need to do any border runs. Come and go as you like.

As Tod said in the first reply, you can convert a tourist visa to a non-o in country.

OK now I see your confusion. The income letter is valid for six month from issue until you take it to immigration for your extension. The extension of stay lasts 12 months.