%downpayment to house for tax benefit

I request your advice for 2 questions below and welcome any other advice you may have about them:

 

I currently live in Chicago and plan to buy a house in Bay Area which I may rent out  (more as investment property) as it is close to my parent's place and they can help me manage it. 

1. I can pay the entire amount with cash. But I understand that I may have tax benefit by taking a loan for some of it. I request your advice on % or amount of loan would help me maximize the tax benefit. 

2. I moved from New York to Chicago in July but have not lived in California in 2025 nor plan to move there this year. I work remotely 100%. I plan to file my 2025 taxes for 2 states as non-resident of New York, domicile and  resident of Chicago Would buying this investment property in California be considered as domicile of CA ? Thank you!