When you're shifting into 2nd, are you getting on the gas and pulling, or are you just downshifting and slowing down?
Sounds like you either have some bad motor mounts, or bad alignment
AND
you probably have warped rotors. Just get some new rotors and pads for the front brakes. If shouldn't take you more than a couple hours to swap out the rotors and pads as a first time thing (adding time for since you said you're new to this). That will take care of the shaking.
For the pulling to the side, take it in and ahve the alignment done. That should solve that.