Alright some answers to the questions presented:
1) We did try using squares and other symbols (cubes and hypercubes - we tried to see whether it has something to do with dimensions) but that did not work.
2) We did not try making it correspond to a map, so that is certainly a new suggestion. However, now that it has been suggested I can confirm that it does not correspond to any map we have.
3) The triangles all point downwards.
4) Circles are crossed. Imagine a circle like this "O" but with an "x" in the center.
5) The puzzle is a 15x15 grid, but the cells are about twice as wide as they are high. I suspect this does not have any significance other than the fact that the puzzle was printed from Excel where cells are wider than they are high.
6) The number 15 or 225 does not have any in campaign or meta-campaign significance as far as we know.
7) There were neither any instructions on the puzzle nor any clues we can relate to it apart from the (exact quote): "Fill in the proper symbols into the blanks"
8) As I have explained in the previous thread, it is simply not possible to go somewhere else or do something else or get some help.
9) Algolei, the symbols you highlighted are correct - they should indeed be there.
As a note, I want to point out that our DM ran an enjoyable campaing, so remarks that he is an idiot and so on are certainly not justified - we played in the campaign for exactly a year now and there were a number of puzzles but there was always the possibility for us to go somewhere else or do something else except this time. Yes, it does suck that the campaign ended because we could not solve the puzzle (and we expressed our pity to the DM), but we moved on to a new one - no hard feelings.