The District of Columbia does require a blood test before a marriage license will be issued. You can marry immediately after your marriage license is issued.
In D.C., as in most states, you must be of the age of consent, not be too closely related to your intended spouse, not be married to anyone else, and have sufficient "mental capacity," meaning you understand what you are doing when you marry.
Yes. In D.C., if you meet the criteria for common law marriage, then you are legally married and will be treated as a married couple for legal purposes, including the requirement that you get a legal divorce in order to end your relationship. In order to have a valid common law marriage, a couple must intend to be married, must live together for a significant period of time, and must hold themselves out as a married couple. If you need more information about common law marriage in D.C., consult an attorney.
Yes. As of March, 2010, the District of Columbia allows partners of the same sex to marry. For trends in same-sex marriage laws, see the article Same-Sex Marriage: Developments in the Law.
To learn more about whether marriage is right for you and your same-sex partner, see Making it Legal: A Guide to Same-Sex Marriage, Domestic Partnerships, and Civil Unions, by Frederick Hertz with Emily Doskow (Nolo).