1) Yes the calendar year is the tax year in US and the FY is the tax year in India. There will be some issues in determining the taxable income and tax liability but they can be sorted out by maintaining the accounts separately for calendar year as well as financial year.
2) The EMI schedule contains breakup between principal and interest components. You can still ask the bank to give a separate certificate for the calendar year also. Normally, banks will oblige for Non Resident account holders.
3) There is no separate rebate or depreciation for self occupied house property. Only in the case of let out properties, 30% standard deduction is allowed.
4) Yes, it includes repairs and maintenance. However, if you are adding new floors / additions to the existing building,they are not allowed separately but they get added to the cost of improvements / acquisition for the purpose of capital gains, if the property is sold.