Don't worry about the cracks but you do have to patch where it's crumbly.
Only worry about the paint that comes off easily, no need to scrape down the whole thing.
Depending on the look you're going for, the whole wall would need a skim coat of plaster.
Condemned, eh? Does the roof leak? Did it? (sad face)
If you are going to contract it out, start making phone calls TODAY. You'd be lucky to find someone who doesn't have at least a 3 week back log during the height of summer.
One of the main purposes of moldings, such as the trim around doors and windows (called casings), is to act as a barrier and seal to wind and water intrusion. Moldings on wall between vertical boards, called battens served a similar purpose. The decorative element was an extra benefit (unless you are an extreme modernist/minimalist who wants totally flat featureless transitions).
Since the days of rough hewn houses, our water and wind protection has improved overall. However casing still are a significant protector, especially against air leaks in cold climates.
Casings provide the protection in two ways - they create a convoluted path for any air to get through by overlapping both the door frame (jamb) and the wall material (plaster, wallboard, paneling, etc); and they they fit tightly and are generally sealed to the other two parts with paint and often with caulk.
Your first approach will compromise both of those features. Your are effectively creating a butt joint with no overlap. The path for air is directly perpendicular to the wall and the casing. The joint will likely crack at some point, even if you mud or caulk. Those seals work well when they are used in a corner that meets at a right angle, with one member going behind the other, not a butt joint. If you add an additional molding, you still have a butt joint along the edge of the original casing that might crack, and you are complicating your profile.
The second approach solves that problem, but getting the old plaster and lath out, and getting a tight fit pushing forward against the in-place casing will be hard.
The third approach seems much harder, but actually may be easier and less time consuming than the first or the second. Once the casings are off, removing the plaster remnants will be much easier. If you carefully score the joints around the casings and where they meet at the top with a utility knife, pry them off using a small catspaw type prybar, pull the nails through the back of the casing, lightly sand the chipped paint off the edges before reattaching, it should be quite manageable. It sounds harder than it is.
Even if you were to crack a molding or two in the process, they can be glued back together, and once painted, will seem whole.
P.S. My house was built in 1869, renovated in 1905, and renovated again in 1999. In the last reno, the above process is exactly what was done, leaving great early 20th century details, smooth walls and tight seams.
Best Answer
I use a sawzall a reciprocating saw with a wood bit and it goes through it like butter. Check for live voltage behind the area you want to cut or you may have some wires to repair , yup done that more than once. I lay the tip lightly on the surface handle and blade touching the wall. Start the saw holding the front of the saw still wile lifting the handle away from the surface, once through hold the saw at a 90 and cut away. I have seen a jigsaw used he drilled a hole big enough for the blade it was a bit slower but a nice reusable cut.