There only visa type that requires a background check is the Non-OA visa, which is not widely used.
If you ended up applying for a visa that DOES require a background check, you absolutely, 100%, will require a certificate. You expect the embassy staff to sign up and login to a portal to view your background check? Not a chance in hell of that happening.
And you also think that the company that provides background checks has never, ever had a single person ask for a certificate? I guarantee they have a way to still provide this.
Seems like you've never been to Thailand before, or never done any type of bureaucracy in Thailand. If you had, you wouldn't have asked basic questions like this. Expect nothing to be easy, everything to require reams of paper, and you to not understand why anything works (or doesn't work) the way it does.
Have you asked your school? Some can convert inside Thailand, and some cannot. For those that can, it can take more than a month between them having to apply to the Ministry of Education for approval, and then you must have between 14-21 days left on your existing stamp at the time that you apply for the ED Visa at immigration. If you don't have plenty of time left available to you, you might have to leave regardless.
Go to a booking website. Find a flight you like. Print out the itinerary and upload it. If they want to see a real ticket they will then send you a request for additional information. Most embassies don't require an actual booking for a visa application.
I'm not sure what you are asking. There is no such thing as extensions when it comes to the embassy. Extensions are done in Thailand at an immigration office. The embassy only deals with visas.
The 90 day non-O visa does not have an insurance requirement.
The 1 year non-OA visa (a completely different visa) does require insurance, as well as health check, background check and other requirements.