Is this humidifier properly installed

It's likely functioning properly. A setting of 6, probably correlates to 40% relative humidity. According to the Owners Manual

Your Aprilaire Automatic Humidifier, is a high precision system that will accurately maintain the relative humidity in your home to a maximum of 45% RH and a minimum of 10% RH.

If the home is at a higher relative humidity, the unit should not come on.

I can only provide anecdotal answers to questions 2 & 3.

2. I have successfully used a few drops of concentrated food coloring, at different places I suspect for leaks in a water softener and its related valves and plumbing. I used 3 different colors if memory serves me right. We had a very slow/unnoticeable leak, apart from the puddle of course. I was able to determine which valve is was based on the color dye that showed up in the leak (blue in this case).

3. The failed water softener in this case did fail due to high water pressure. I would see if there is any manufacturers rating for the humidifier's working water pressure. There is no telling what parts, valves or plumbing inside the unit make be deforming/failing under such high pressure.

Good luck in your troubleshooting and fix.