R13 or R19 Insulation

I want to add a bedroom in the corner of my finished basement. I will only have to frame two walls. I have a drywalled ceiling (1/2" drywall) and Burbur carpeting on the floor. My questions to you are Do I need to cut away the drywall where the header of my wall is going to meet the ceiling rafters or can I just nail it through the drywall into the rafters? Also, do I have to cut away the carpeting on the bottom plate or can I let the bottom of the wall rest on the carpeting and attach nail it through the burbur? Thank you for your time.

I am about to start framing my basement walls in a day or 2 and the other day when I was in line at the home depot I opened up one of their how to books and flipped to the section on framing a basement wall. In there they had something about putting a sill plate nailed to the concrete screws and then framing the wall and screwing it to the top plate but having the wall a little bit shorter then the opening between the top and bottom plate. Then they had between the 2 bottom plates pins to hold the wall from being pushed out. Long story short the reasoning behind doing this was to leave a gap for if the basement floor heaves or settles at all while still making the wall as strong as possible. Is this common practice and should I be doing this myself or is it overkill? My floor had heaved in the past but I believe it was only in the first few years as the old finished basement subfloor was built level over this uneven floor over 20 years ago and it was still level when I took it out.