2017 Hyundai Tucson Not Accelerating

I've been having an issue with my brakes for months now. I even took it to the dealership to have them test drive and inspect them, and they said everything was fine...clearly not. No matter what speed you're going, or what pressure you apply to the brakes, there's a jarring bumpiness that sounds and feels like the rotor's are shot or something. It's mostly felt in the front, under your feet. There doesn't seem to be any grooves in them and the pads are fine, so I'm looking for some help on what this could be and how much it would cost to fix, before I take it in and they just start ripping things apart. I've also recently started getting a very jumpy, sluggish start off whenever I'm stopped, like at a light or something, and start to move again. It came on very sudden...one day it was fine, the next, this was happening. And it seems to be getting worse. Again, what could this be and how much would it be to fix? Thanks for any help you can provide!

does the 2016 Tucson have an emission pump; there is a noise coming front the right side in the engine compartment at slow speeds/driving slow 15-20mph and sometimes idling. There is no noise at higher speeds 30-60mph. other than that there is no major problems with the car/vehicle