These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Fridge Brilliance: In Free Willie, Fraser mentions a half-remembered thing his father once told him when he was very young about sewing your wallet to your underwear, then quickly moves to a more relevant topic. A few episodes later, in Manhunt, Buck tells Fraser a story about Bob Fraser trekking out into the wilderness to the place he nearly died previously (rescued by Buck) to recover a wallet that young Fraser had made for him. Maybe that experience was why he started sewing his wallet to his underwear.
That is correct: an unloaded gun would still be seen as illegal under Chicago law. However, as a RCMP Officer, he would be permitted to carry a loaded firearm in the States. Fraser should have been well aware of this considering his familiarity with all the laws.
In A Cop, A Mountie, and a Baby, the episode ends on Ray and Fraser bantering and walking off into the distance... or rather, walking onto what appears to be an active flightline at their local airport. It's not really clear where they were planning to go.