It depends. If you're getting a visa that requires health insurance you'll have to buy Thai. If not, you may find better value getting at home. For Thai based insurance misterprakan.com is a broker for all the main issuers
I understand your reasons for wanting to stay but I'm not sure that would be enough to be granted a covid extension. You may as well try though. Can't see you've anything to lose by asking
Try mrprakan.com brokers. If you choose the Tune insurance that can be cancelled and refunded if you dont get the visa, however it isn't necessarily the cheapest option, if that's what you're looking for. However, if all your other paperwork is in order then there's no reason why you won't be granted it
Lufthansa should be making an effort to get you into another flight at their expense. Their local number is +66 2 056 6868 but they do regular office hours so call now
it's Thailand. They're more suspicious if you're not sweating. I need to Google what 2kg of protein powder rupturing in a stomach does to the sweat glands