Shudder during breaking (new rotors and pads)

Hello,

Every time I applied the brakes on my 2011 Toyota
Corolla I felt a shudder, the rotors and pads were
pretty much new, but I replaced them anyways
thinking it may be a warped rotor. After replacing
them, there is still a shudder while applying the
brakes. The calipers have new sliders that are
sufficiently greased, and on installing new pads, the
pistons did not resist much while pushing them in.

The car is new to me, I purchased it this winter. I
did notice times that when applying the brake the
abs was over sensitive and would lead to a barely
working brake (I believe this was snow build up).

One last thing, I noticed a clunking noise a couple
months after buying the car, and it turns out the top
caliber bolt was missing so the caliber was
swinging out and striking my steel rim.