No way to prove a lot of stuff, except that a lot of people seems to be genetically unable to STFU.
Used to work with drug squad, and I was always amazed at how someone would get caught with a bag of weed, wet their pants, and roll over on every one they knew. Folks would come in, "I never thought Billy Bob would snitch on me."
I can take Billy Bob's cell ph. records and show that on a certain date and time, he drove to your house. I can take your credit card records and show that you were buying ammo of a certain caliber. I can take your cell ph. records/ODT chat records/email and see all sorts of stuff. This day and age, it's really tough to set up a sale without leaving some sort of trail.
What happens on the internet is satire, dont you watch youtube? Comments here are like rap lyrics, not legally binding contracts or admissions of guilt.
Good luck with all of that circumstantial evidence that you gathered. If the police were as competent as you're pretending that they are, they would be too busy catching thieves, rapist and child molesters to worry about gun transfers.