1. There was an investigation. It began as the BB gun. It then became an investigation into the muzzleloader.
2. If they were not aware you had it, or had bigger fish to fry, yes they may possibly wait months to get around to you.
3. Again, provide the backing case law or statute. I have never heard of such a restriction. The allowance for police deception is usually very broad and I don't see anything wrong with anything done here. There were no apparent lies told. Perhaps deception if the officer used the BB gun as a pretext for making contact but even then, not what a court is likely to consider illegal deception.