Cracks on Ceiling and Wall
The wide spots are where the tape came loose and this could be from a leak or bad install in the first place. I don’t see any damage to the Sheetrock so it probably is not a chronic problem. The crack in the corner looks to have air flow, notice the dark area with lines close to the crack. I have seen this around air plenums many times. From what I see they don’t look bad as a real concern about the structure. Repair work to fix these is more of an art than hard because it can be tough to match the texture. I would clean them up get a small tub of joint compound a roll of “paper tape” some sandpaper or Sheetrock sanding cloth and a can of texture. A wide putty knife is really the only tool needed because it is small areas but a mud tray could be handy and a pole sander can make the job easier. Don’t get hot mud or a fast setting type it is harder to sand and takes more skill to apply ( it looks like some one may have already made this mistake. 
So how big is the project? It depends on your abilities, I would say it is an easy fix however some would say impossible. For a new to diy an hour of online research should be 45 minutes more than is needed to learn how to do it. Maybe an hour of prep work to clean things up. And since there are multiple surfaces flat and corners maybe 2 hours on the first pass and a quick sand then a final coat 30 more minutes prior to a quick shot of texture and painting.  This could be broken down into a bunch of tasks 30 minutes or less you don’t have to do it all at once and usually over several days. A pro could probably have it done in about an hour maybe 2. So it really is not a big job at all and although a bit like art it is a great skill to have. I have seen people pay hundreds for repairs that only cost 20$ in parts (mud, tape and Sheetrock) and took a pro about an hour once set up.