In full fairness to Parallels, I want to describe the solution found for the issues identified in my original post. I opened a support case with Parallels, and was advised as follows:
1. Go to Actions->Take a snapshot.
2. Go to Configure->Options->Sharing->Uncheck the Shared Profile: Share Mac files with Windows.
3. Go to Control Panel->Programs and Features->Uninstall Parallels Tools.
4. Go to Configure->Options->Sharing->Enable or Recheck the Shared Profile.
5. Start the Windows virtual machine.
6. Install Parallels Tools under Actions.
After completing this procedure, the herky-jerky behavior of windows programs was resolved, as were the issues with opening programs, including default programs. I can't tell you why it worked, but it did. I'm just disappointed that finding this resolution required initiative by me rather than by Parallels.