In Fairfax County the non-lender owned townhomes and detached single family homes in good condition are sold mostly on the assessed value lever. If these homes have modern updates and upgrades, they will generally sell for a little above the assessed value, however some upgrades can be very impressive, and the sold price will be 10%-13.8% higher than assessed value (13.8% was the highest I saw in this market).

REO and short sales townhomes and single family homes usually sell under assessed value, the price will strongly depend on the condition.
The highest difference I saw between assessed and sold value was -73.6% for the home which was damaged by fire. It was listed though 80% lower than the assessed value (so it sold for more than it was listed for).

A lot depends on location and its peculiarities (major routs, Metro, places of business concentration, schools, parks, shopping centers, waterfront, new construction close by, etc).

The condo market is a different story. Condos deserve a separate page. The main idea: the price of a condo needs to be estimated based on the price of condos within the same condo association, with consideration of prices of similar condos in the closest area and also taking into account fee simple property prices in the nearest location.

All the best!

That depends on multiple factors and varies from one local area to another across the country.