Ceiling – How to locate the ceiling joists in the kitchen addition

The 2X4's you are looking at are collar ties attached to the end of the rafters and span wall to wall. They are really only strong enough to support ceiling materials, not a live load. The new floor joists will need to rest on the upper wall plate (load bearing) adjacent to a rafter, and cross supported.

The items you need to determine are span, joist spacing and material to be used as floor joists. This link shows a chart in feet and inches for you application: http://www.the-house-plans-guide.com/joist-span-tables.html. Even on short spans, I would never go any smaller than 2X8's to assure a flex free floor.

The second issue you will face is insulating the roof. The size of your rafters are going to dictate how much insulation you can install. If they are less that say, 2X10, you will not be able to get a good R-value. You may have to consider maxing out the cavities with blanket insulation, then also adding some 2 inch rigid foam sheets over the entire field to increase the total R value. You could then install strapping (purlins), with long screws, to mount drywall to. In this kind of roof design, there would be no venting required. This is a very common type of construction on cathedral type ceilings. 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.