If you are not legally married as of 12/31/2019 then you can file either as Single or Head of Household if you are eligible. See this TurboTax support FAQ for HOH - https://ttlc.intuit.com/community/family/help/do-i-qualify-for-head-of-household/01/25539
Can you both use the same address? Yes
Can your ex spouse file as Married Filing Separately? NO, if he has not remarried he can only file as Single
