If it's a gift, then the giver of said gift should be filing IRS Form 709 - Gift Tax Return, with the IRS. Note that nobody will pay taxes on the gift. It's just a legally mandated reporting requirement for any gifts given in a single tax year that exceed a value of $16,000.
When they gifted you the property, they gifted you everything; original cost basis (including any property improvements), as well as depreciation already taken. Since this is not a reportable/taxable transaction on anyone's tax return, you'll use their original cost basis as well as their original in-service date for the property and any property improvements, and the depreciation they have already taken on the property is also transferred to you.
under "placed in service" for this rental property, should I be entering the date the property was transferred to me,
No. You'll use the same date your parent's placed it in service. Doesn't matter that it may have been years ago.
For the cost, would it be the fair market value or the amount my parents paid for the property
Yes, which is to say, it will be the same cost basis as your parent's used.
For the land value, the city records shows the land value fluctuating from year to year
Assessed tax value is irrelevant, and is not reported on a tax return at all. It will be the same as what your parents used.
