First problem, strange file name: "~" is a joker character in AmigaDOS. It must not be used in file names. You cannot delete the file because you cannot enter the "~" as a part of the file name, it is always interpreted as a joker by the delete command. You have to use another joker to replace it. For example "delete ?backdrop" will delete both .backdrop and ~backdrop (every file with one character before the backdrop). Or "delete ~(.)backdrop" will delete all files ending in "backdrop" but not if they start with a ".".
Second problem, not opening windows: do you have some patch installed which influence the appearence of windows, e.g. PowerWindows or VisualPrefs or Birdie or something like that ? Maybe also MCP could be a cause of this. Remove all patches. Does ARTM tell you what the programs are waiting for ? Does opening Workbench drawers work ? Does the disk icon appear if you insert a floppy disk ?
Bye,
Thomas