No. You must show proof of your location through an entry stamp in your passport. And the embassy do spot checks by scheduling interviews and checking your passport.
You can't just pick and choose the embassy you apply at. You have to physically be where you are applying at, and must remain there for the duration of the application process. And Paris is known as a very bad embassy that can take very long time (more than 1 month) to process visa applications.
So get a long term visa and you can stay as long as you want? Obviously. But if you're not willing to apply for extensions and do paperwork, then go elsewhere. That's a part of living anywhere that's not your home country.
Once you get your visa you don't have to keep it anymore. Unless you apply for an extension from immigration, but you shouldn't do that as they don't like issuing those extensions and make it incredibly difficult.
In Chiang Mai you will be pulled out of line, and taken aside to fill out some paperwork, asked to show 20,000 baht, etc. Best to fly into somewhere else.
There's a reason no one uses the non-OX visa. It requires 3 million baht in a Thai bank account. There's only one Thai embassy in all of the world that allows people to use their home bank account to show the 3 million baht and that embassy is in Australia.
And I'm not sure why you are asking about Paris and also about Taiwan. Where are you applying? That's the only place that matters. And the OX visa can only be obtained from where your passport is from or where you can prove you have permanent residency.