Here is an article about domicile.
https://accountinginsights.org/what-is-the-illinois-183-day-rule-for-tax-residency/
Here is California's web page.
https://www.ftb.ca.gov/file/personal/residency-status/part-year-and-nonresident.html
Your domicile is determined by where you live most of the time and where you consider your permanent home to be. Owning investment property in any particular place does not change your domicile.
However, if you are a non-resident of California, you will still owe California state income tax on any California-sourced income, such as a rental property in California (assuming you actually show a net profit, your goal is to show a loss). You will need to file a CA nonresident return to report the rental property income and expenses, in addition to an Illinois return to report all your world-wide income (plus a part year resident for NY, at least for 2025).
Regarding mortgage, the interest you pay is a rental expense, but not the principal. So you would not deduct anything for your down payment, but you can deduct the interest. Ideally you want to have a positive cash flow but show zero taxable income or maybe a loss, by matching your rent to your expenses including depreciation. However, the exact math is not something I can help with, you would want to talk to an experienced accountant who can look over the facts of your situation.
Mortgage interest is not going to be deductible as an itemized deduction on schedule A unless this is your personal second home, meaning there are limitations on the number of days you could rent it out (I don't know the exact rules but someone else will).
