Make sure the window is level first. If its not and you level the window sill, it might be noticeable right away. It depends on how much.
If it is ok, then place a long level on the surface and check its bubble. Then raise the right or left side to center the bubble. Use a pencil and mark a line on the window frame indicating the spot where you need to add some shims.
Do not use shims that are about 1-1/2 inch wide. I have seen shims that are about 4 to 6 inches wide. use these instead.
Then lay your windowsil on it and add more shims to support it.
Before you secure the windowsil, place your level back on it and check to see if it is still level.
If you have a table saw, cut some thin sticks off a scrap of 1x that will just fit under the edge of the replacement window, and place them on the rough opening every 16" or so. Adjust the width of those rips as needed. It should be sitting on shims anyway.
If you use tapered shims, you always need to use them in pairs, one pointing one way, one pointing the other way, in order to keep the stool from tipping. You cut the shims to the size (length = thickness) you want then slide them back and forth to adjust how thick they are when placed together in a pair.
Your stool could be made from a poplar 1x4, or 5/4 if you can find it. Don't know where you are located. You probably also need to cut jambs for the sides and top after that. (out of poplar 1x4 again). Then casing. They sell it in preprimed but often priming it yourself is a better quality primer.
Your question about adhering wood to block is top vague to answer. Tapcons.
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