Can you have passive income like renting part of property out? Will it affect a rating of TDIU?
Yes, you may have passive income with some restrictions. This can get really complex in a heartbeat but in broad terms, you are allowed income that isn't derived from gainful employment. Gainful employment is generally described as that work that earns you a taxable income of more the the federal poverty level. You can rent out a piece of property and unless it's a part of a business you run and derive an income from, no problems.
This is also true of income like inheriting a fortune from your poor Aunt Tillie when she passes and leaves her vast wealth to you or winning the Lotto. Neither of those are gainful employment and won't affect your TDIU rating.
There is no form to complete or any reason to seek permission to earn a small income. VA tracks your taxable income by associating your VA file with your IRS and SSA data so if your taxable income from gainful employment rises to more than the poverty level, VA will be in touch with you to offer a solution. Good luck.