1. I think you must apply for an FM-2 locally at the immigration office. Not in the US.
FM2 Immigrant resident visa — Inmigrante » Jaltemba Jalapeño
2. FM2 applications are only available locally. The office is in San Jose.
3. You can buy a car, but only a US plate can be driven legally by a foreign driver. Mexicans are prohibited from driving foreign plated cars.
4. You just have to renew the registration on a US car in the state it's registered in. South Dakota is a state where a lot of US cars are registered.
5. I hope your Spanish is good, because the test is in Spanish. They do allow translators. I believe you must have a MX drivers license to drive a MX plated car. The exception is for rent-a-car vehicles.
6. Yes you can buy insurance locally.