As expected, President Reagan signed legislation ending the Federal Housing Administration's three-week shutdown. The agency's acting head, Silvio DeBartolomeis, notified the agency's field offices and major lenders to resume processing government-insured mortgage applications. The bill that Reagan signed extends the FHA's statutory authority to Sept. 30 and raises the agency's credit ceiling to $83.9 billion. However, the continuing demand for FHA-insured mortgages means that the $9.5 billion in new credit authority will last only until July 25, DeBartolomeis said. In another housing-related development, the National Assn. of Realtors said the sale of existing homes declined 3.4% last month to a seasonally adjusted annual rate of 3.45 million units.