Married spouses living in CA and MN

My husband and I plan to file joint federal return, but unsure what to do for state returns. I moved out to CA recently for a new job, while he plans to keep MN residency but split time 50/50 between MN and CA (working remotely on his MN-based job when he's in CA). My questions are:

1. Are we allowed to file separate state returns?
2. What filing status will I be for CA?
3. How many allowances should I claim for CA?

Thanks so much!