I'm assuming when you say put a rental property in your IRA you mean purchase a rental property with money inside your IRA? If you already own a property you can put it in your IRA. There might be some way where you could transfer up your annual limit of value in to your IRA each year but you would need a current value and subtract that value and would be very costly doing appraisals each year as well as I think easy transaction to cause your IRA to lose it's tax deferrred status if done wrong.
Most of your questions appear to have been answered in the 2nd response but a couple points to think about on whether to own in your IRA or not.
While a property in your IRA will cause you to avoid paying income taxes you will lose the ability to depreciate your property which for most is a great advantage and reason they like investing in real estate.
Also it is very difficult to obtain non recourse financing to leverage your purchase inside your IRA. There are a few companies that offer it at competitive terms but they are very selective on their loans they will entertain. Leverage is another great thing about investing in real estate and the terms and availability are much better outside of an IRA. Also when you use leverage you get the further advantage of being able to write off the mortgage interest.
Since it appeared that one of your primary interest in owning inside the IRA was to avoid taxes I think it would be good to get a good understanding of what a typical cash flowing rental with leverage ends up looking like when you factor in depreciation and an interest write off. Very likely to be cash flow positive but tax neutral.