Must you have permit to homebrew beer in Michigan?
Not for your personal consumption. Each individual can brew up to 15 gallons a year for their own use. Anything over that requires a license.
There are a lot of factors to be considered. If the bottle is stored in the dark and a cool place, it can last for several years. If it is a homebrew or from a local brewery that doesn't filter the beer, the flavors can be greatly affected by the living yeast. There are some types of beer that actually improve with age.
Yes, but only in certain situations. Beer can only be acquired at a bar, restaurant, licensed beer store or distributer. Beer can not be sold before 11 am and a retailer will require a special permit to sell on Sundays. Several supermarkets have attached restaurants, where they can sell take-out beer, but it can not be sold in a normal grocery store.