Sounds completely bogus, did you ever have a long overstay previously? Are all your entry exit stamps correct? I think your name got confused with someone else. This is a bizzare scenario.
They are really finicky in Vietnam as to showing proof of your current location so once you do that and it satisfies them I don't see why you can't travel around a bit but just be ready to be called in for an interview.
yes you must apply outside of Thailand and you can apply in any country that allows you to apply so check the website of the embassy you wish to use to make sure that you have eligible residency. Again an ambiguous answer, why dont you say exactly what country you want to apply in, and exactly what passport you hold?
They want to see you have viable provable past experience even if it doesn't make money. You can't alakazam I'm an app developer. They might also want to see you pay taxes and have tried to legitimize yourself. It's all in the presentation of your cover letter describing what you do, how you do it, why a workation place like Thailand suits you.