What causes this strange noise/feeling when i push my brakes?

If you replaced the pads but did not resurface the rotors, it may just be the pads hitting a high spot on the rotor. You will not see this unless you take the pads off again. Or you may have a frozen caliper. Did you grease the caliper slide pins when you did the brakes? I doubt the brakes have anything to do with the other problem.