6013(g) election in the context of DC taxes / foreign earned income exclusion v. foreign tax credit

I am a US citizen and just got married to a non-US citizen in the US on a G-4 visa. My spouse is exempt from paying tax in the US on the income she receives from the international organization she works for. We are thinking of making the 6013(g) election to file jointly.

*Question*: Are we able to file as 'married, filing jointly' for the purpose of DC taxes, as well? How would I file my DC taxes if we were not able to make the 6013(g) election for our DC taxes?

 

Assuming we were going to file jointly, my spouse has a small amount of income from an investment in another country. I understand that this income would be subject to US tax.

*Question 2*: Would we want to take advantage of the Foreign Earned Income Exclusion (FEIE) or the foreign tax credit? How would this income be treated for DC tax purposes?