The 2nd pic looks like the "crackle" texture is intentional, but the fact that it ends in pics 1 & 3 leads me to believe that this is simply a failing paint job. I'd guess that it would scrape off reasonably easily. The problem is that it may take the paper covering that makes up the outer layer of the drywall with it when it departs. Then you no longer have drywall, you just have chalk (effectively).
Since the landlord has give you permission to do the painting yourself, I'd follow up with written notice that you're going to try to scrape the old, cracked paint off, but are concerned that it could cause damage to the drywall, and request written permission to proceed despite the risk and a commitment to replace the drywall (at no charge to you) if your attempts don't work/end up causing damage.
That way you're covered either way.
I'm somewhat surprised that this was rented out to you like this, especially since you mention "management company". Usually corporate owned places get a repaint of builder's beige between renters if there's any significant damage or modification (like a questionable paint job) by the previous tenant. If it was an individual who owned a house or two that he leased out, I could see that happening.