1/ Washington is a unique case with an obvious solution. When the U.S. was created, most political power resided in the states. A national capital was deliberately created from land donated by Maryland and Virginia that would not be part of any state, and therefore not subject to a state's authority. The Virginia land was returned to that state in the mid-1800s, before the Civil War. The rest of the District of Columbia could be returned to Maryland, apart from a small federal enclave that would basically include the Capitol, the White House and the Mall. The current D.C. residents would become residents of Maryland and vote in Maryland's federal and state elections. "Retrocession" has been widely discussed for decades; it's not a particularly radical proposal, but several problems are associated with it, including the fact that the 23rd Amendment guarantees D.C. three electoral votes and questions about whether Maryland would assume the D.C. government's pension obligations.
2/ There is nothing in the Constitution that requires states to deliver their electoral votes to one candidate on a "winner take all" basis, and two states choose to do it differently. Most of the problems of the Electoral College would be solved if the states simply allocated their electors in proportion to the popular vote, or as close to it as possible if fractions weren't permitted. In Florida in 2000, there would have been no Constitutional crisis; Gore and Bush would each have gotten half the electoral votes. But obviously the states that benefit from the current system won't support any changes.