You can enter the rental even with no income as long as it was available.
Yes, enter the interest that was incurred while you lived in each house as Home Mortgage Interest.
Enter as only one Form 1098 and add the interest from the first 9 months of house A on that 1098 screen as long as none of the loans were home equity or refinanced with cash withdrawals. (As long as all the interest was used to buy, build or improve the homes)
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