I'm not sure how much help we can be, but maybe we can get someone from the Foldit team involved. Here's a little bit on how the game version works in the mean time.
In the game version, files with the "ir_puzzle" extension specify the properties of a puzzle as keyword-value pairs. The "PDB URL" keyword specifies where to get the rest of the puzzle files, and contains the URL of a zip file on the Foldit server.
The game doesn't use PDB format directly. Instead, the download package contains a file with the extension "opdb", which probably means "obscured PDB". It's a binary file, not readable by humans. A download package contains several more files, some obscured like the "opuzzle_setup" file, and some in plaintext, like the "params" file. The exact mix of files depends on the puzzle.
All these files are related by the node number on the Foldit website. So puzzle 1699 is node 2007949, which expands to https://fold.it/portal/node/2007949, it's page on the Foldit website.
Puzzle 1699 has the following setup files:
0002007949.ir_puzzle
0002007949.ir_puzzle.opdb
0002007949.ir_puzzle.opuzzle_setup
0002007949.ir_puzzle.owts
The first file, 0002007949.ir_puzzle, points to the the zip file on the Foldit server that contains the other three files. The zip file contents are named like "PUZZLE.opdb", which ends up as "0002007949.ir_puzzle.opdb" once the game client unpacks things. So the "PUZZLE" part of the name for each zipped file gets replaced by the name of the ir_puzzle file.
I have no idea how applicable all of this is to standalone Foldit, but everything ends up in the same directory as the main Foldit executable, which is foldit.exe on Windows. (This directory can get a bit cluttered as a result.)
I'll see if I can find more info on standalone. I think there were some instructions distributed a few months ago, but I'm not sure they contained this level of detail. I think that unlike a plain viewer (Jmol or Pymol), standalone Foldit may need more than just a PDB file to get started.