Do I need to nail crown molding to ceiling

Crown moldings, or any corner trims really should be nailed to a stud, not simply into unbacked drywall. Without good support, the molding will warp out from the wall causing gaps in coverage to open along the edges.

With real crown, there is a hollow gap behind the molding as only the top and bottom edge touch the wall. The wider the molding, typically the deeper the void behind them. This gap results in having to use longer nails to reach the wall and support wood behind the sheetrock.

One method that works well to make installing the molding easier is to first install a backer/nailer to the wall. Depending on the size of the hollow behind your crown, cut or rip some scrap board, plywood or even strapping, then nail it along the top edge of the wall against the ceiling. You can shoot as many nails as you want to assure the backer if firmly attached to the studs or wall plates, as it will never show anyway. Now, when you go to nail your crown up, there will always be a solid wood backer anywhere you shoot a nail. You can also use shorter nails, or at least not have to use extra long ones. This method is also helpful when your walls are not perfectly flat and an extra nail is necessary to draw the molding in tighter to the wall in irregular areas. Good Luck

Go ahead and place the drywall over the top edge of the crown moulding. Sounds like the wall was already re-plastered with it in place. If you tried to remove it, you may end up re-doing the walls as well. Even forgetting that, it's almost impossible to remove moulding without sustaining some loss. Without replacement material available, removal with intents of preservation is extremely risky, especially with stain grade material. You don't want to go there.

If your joists were flat, you'd still only need to shim down the first 4 feet or so along the walls, no one will see the resulting slight slope. Keep this in mind when planning your shims. It doesn't have to be perfectly flat, unless that gives you pleasure. You also don't need to shim to completely fill the gap. An 1/8" gap makes a clean shadow line that is not detrimental (assuming it is perfectly uniform) at all. It also makes finishing easier. The taped joints of drywall are normally not perfectly flat, despite the tapered edges. There is a slight bulge which is usually invisible. But against straight moulding, depending on the profile, this bulge may be visible. You might consider grinding down the edge tapers at the board corners against the wall so the joint tape can be completely buried and the yet the joint against the moulding can still be perfectly flat.