1) You will need to file a part year return for both MN and Iowa, if you live in both states for part of the year.
2) It was most likely because you had income then being reported for both states but you did not have taxes withheld for those states. If you are a full year resident of Iowa, then all of your income from both states for the entire year is taxable in Iowa. If you are a part year resident, then the income earned during that time is taxable. If you maintain an LLC in Iowa and that LLC makes money throughout the year in Iowa, that money is all taxable to Iowa as it is Iowa sourced income.
3) Paying the mortgage on your dad's house and being a co-borrower does not make you a resident of that state. If you have 2 houses, one in each state, you are a part year resident of both states. If that has been the case in past years, and you filed part year residency for both states, then there is nothing you need to change.
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