The answer is Yes to both your questions.
If your domicile (your main, primary home) is in VA, and you maintained a place of abode in DC for a total of 183 days or more during the tax year, then your situation is one of dual residency. You are both a statutory resident of DC and a domiciliary resident of VA.
In this situation you must file a resident tax return (reporting all your income) in both States, but VA will grant you a credit for the taxes you pay to DC on the income taxed by both. See Dual Residency in this VA tax reference:
https://www.tax.virginia.gov/credit-for-taxes-paid-to-another-state
**Answers are correct to the best of my ability but do not constitute tax or legal advice.