You have a lot of questions that you need to sit down with a local tax pro before you do anything to see what your state rules are on LLC filings. Unless you incorporate or are in a partnership, getting an EIN and register with the state will mean nothing as far as your tax return goes. All those incomes will still be reported on the Sch C or Sch E. What you really need to do, to CYA, is have a really good insurance policy for the rental. An LLC designation will not save you from a lawsuit.
If you do incorporate then you must take a resonable wage and file payroll tax reports quarterly... this may not be in your best interest. So seek local guidance on all your options.
