Married couple living in different states, filing jointly. Spouse does not work. Child lives with Spouse. How do we claim dependent?

My spouse and I live in separate states, CT and MN.  I am the sole wage earner, and my spouse has no earned income for 2021. Our 10 year old child primarily lives with my spouse. 

 

(1)  From my research here, it seems that we can still file a "married filing jointly" return.  Is this correct?

(2) Since my spouse has no income, I believe he does not have to file a state tax return.  Is this correct?

(3) Most importantly, how do we correctly claim our son as a dependent, since he lived with my spouse for more than 180 days of the year (and not me?)