Hi
What are you using with the Pk3, old Mplab IDE, MPlabX or Pk3 Stand alone program ?
Whichever it is, there is a tool /option check box to select Target power only , so that should ensure its only programmed with target voltage.
Again , whatever IDE/program you are using, there is a box to specify what VDD voltage you want the Pk3 to supply, have you changed that ?
Regarding running the LCD on 5v, cannot say with 100% cetainty, but I believe under certain circumstances the LCDs 5v can run back down the data lines to even power up the 2520, so there is a chance that it may have damaged the radio chip.
With your whole circuit powered with 5v and 3v3 have you checked what voltage shows on the 3v3 rail ?
As for you circiut only running from Pk3 power, have you programmed in Debugger mode ? have you got Mcle set to off or with 10k pull up ?
Using fuse wire - sounds a bit dangerous being uninsulated ?