You can deduct all property taxes you pay on schedule A, but this is subject to the $10,000 state and local tax cap.
You can't deduct the property taxes on house #2 as rental expenses on schedule E because the home is not currently available to rent or rented. Once you list the home for rental, your taxes from then on become rental expenses.
You can't deduct the mortgage interested on home #1 that you used to pay for the renovations to home 2. That's equity debt and is not deductible as personal mortgage interest on schedule A. Once you hold home #2 out for rental availability or rent it, you can deduct the interest as a rental expense, but not the principle. And you can only deduct the interest as a rental expense if you maintain traceability between the loan and the improvements. If you start taking money out of home #1 for other expenses, then it becomes much harder to trace the interest directly to the rental improvement and your deduction is at risk if audited.
You never deduct renovation expenses. They become part of the new cost basis of house #2 when you start claiming a deduction for depreciation on house #2 when you hold it out as a rental.
