Multiple State DE & IL

Hi,

I am a DE resident (home, license, etc.) but worked in IL until end of March and worked from home in DE because of COVID.  I had an apartment in IL for convenience, but ended my lease at the end of May as I continued to work from home for the rest of the year.  I notified my employer that I no longer rent in Il and to switch my state withholding to DE.  It took my employer until the end of September to make the change.

1. In turbotax, I am asked when I started living in DE and that was flagged when entered 1/1/20 as I stated that I had lived in IL, what date should I enter?   How should I answer when asked If I lived in another state?

2. When I divide my income what do I base that on: a) March 31, B) end of May when I ended my lease or c) when the withholding change in my paystub which is essentially October 1?

3. If October 31, that means I am not a DE resident which I am and what state is my residency based on?

Thank you