Although this is late in coming. I came across this forum since I was experiencing the similar problem (i.e. humming noise when braking after installing new brakes and rotors). After replacing my brakes and disc rotors on my 07 Edge, I started experiencing immediately an intermittent humming noise when I hit a brake or coming to a stop. And sometime even when I start going at slow speed coming from green light up to maybe 30 MPH. The noise goes away when I am going a little faster (i.e. over 40 MPH). I also noticed that my rotors were over-heating. Looking at different blogs, people mentioned about wheel bearing, or tire not seating well or lug nuts not tighten the right way... I tried all that to no avail. I even went on to buy new new pads (BrakeBest) to replace my previously installed new pads (Wagner) given that I have always used BrakeBest in the past.
But finally I came across this site (https://www.motor-works.com/blog/caliper-slide-pin-boot---what-is-it-) that explains the part that I was overlooking. The caliper guide pin boot was the problem. On my 07 Edge, the bottom rubber pin boot were broken and therefore since they just don't seat outside like the one on the top side of the caliper, they go through the hole on the caliper bracket, every time I insert the caliper guide pin, it was getting stuck and I was forcing it. Given that the caliper guide pin was made of rubber, it was making the caliper not able to float making the brake pads to stick against the rotors and therefore causing noise and overheating.
After replacing the caliper guide pin boot and making sure the pins are greased with synthetic grease, the noise completely went away. I was able to reuse the same brake pads since they were still intact.
