As I understand it, the short answer is "no", on all counts, except for certain cases where the Y-DNA and Mitochondrial DNA can do the job.
1) Your own personal test is basically redundant with those of your parents', as far as I know. It's cool to see what you got from who, but I don't think it adds anything in terms of confirming or triangulating anybody.
2) In isolation, your parents' DNA can help your cousins tell which side some of their DNA comes from (and therefore, which side of the family many of their matches are on), but that's a "one way street". Their value to YOU is in the extra DNA from your grandparents that they have - they might be able to triangulate with people that your parents can't, just as my own brother matches some of our 4th cousins that I don't match. They also confirm your grandparents, but you'd get that with any further confirming and triangulating anyway.
3) To do what I think you're talking about, as far as seeing if a match is on a given grandparent's side, you would need your parents' cousins, not your cousins.
4) 4 generations back (from your parents, so 5 back from you) is 3rd cousins, so if there are matches in their generation (or above) you don't even need to triangulate for confirmation (roughly speaking) - which means you only need ONE matching second or third cousin. With the right matching distant cousins (at least TWO), you might be able to confirm further back than even 5 generations, through triangulation (again, that's 5 gen back from your PARENTS, so pretty far back!). But, again, you need specific additional distant cousin matches for that, vs what you're talking about (which only confirms as far as your grandparents).
I hope that helps!