Assuming the shim doesn't extend past the top of the stem, you'll be able to use a normal 1,1/8" top cap
And if it does, just add an extra 1⅛" spacer so you can use a 1⅛" top cap anyway. You don't want to be using compression of the shim to adjust your bearing preload.
Assuming the shim doesn't extend past the top of the stem, you'll be able to use a normal 1,1/8" top cap.
No idea about the best approach for the star nut, but @roboto has a CP thread where one method is discussed.