In all of the high-rises in Foggy Bottom, the fee is payable monthly.
As to what it includes, that depends on the community.
In co-ops, the fees include the real estate taxes. In condos, they do not.
In older communities, the fees can include some, or all utilities.
In newer communities, the utilities are usually separate.
In the Watergate, the fee is going to include RE taxes, all utilities and even basic cable.
In the Ritz, electric, gas and cable are going to be separate.
In listings, they usually have a line "Condo fee includes" and then list what it includes, so you can check this out on a case by case basis.
Hope this helps.