You can still get federal aid and scholarships from the school. You will not be able to get aid from the state of Ohio or the state of Michigan.
State aid is only for residents of the state who are attending an in-state school.
You will also be paying out of state tuition. You will not get more federal aid for choosing a more expensive school.

Possibly.

But what you won't get is the in-state tuition discounts given to ohio students because you are from michigan.