Yes. Since Michigan and Indiana are reciprocal states, you just need to download and complete form WH-47 to be granted an exemption form paying Michigan taxes. With this exemption, no withholding is taken out of your paycheck for the state you work in.
No. Even though IN had your money, you were late with the Michigan payment.
Since Michigan and Indiana are reciprocal states, you need to complete form WH-47 and give it to your employer so he will stop withholding INDIANA TAX. He may be able to withhold MI tax instead. If not, you should send in quarterly estimated payments.
If you paid IN county income tax, in addition to state, you cannot get that refunded but MI will give you credit for that on the MI return