I live in Michigan but also own a home in pa.

Can I register my car in pa and get penna plates for it and buy car insurance in pa?

That raises a "domicile" issue. Insurance is based on where the vehicle is based and primarily operated. If there is a suggestion of collusion to get a cheaper rate, you may find a claim denied. Can you afford that?

You would register your car, get the plates, and purchase your insurance from the state where your car is "at" where is it physically ? That is the question.

As mentioned... get it where the car spends its time or you can find yourself with a canceled policy, denied claim and big trouble.

Where you spend 6 months and 1 day per year. Of course plenty of people use a cheaper rate (and maybe a cheaper tax too; mine uses the mil rate of my property tax) of a cheaper state where they own property, but if it's a big enough claim, the insurer will investigate. I don't know anyone who cheats on this who has more than the minimum insurance on an old car.