Patching and Plastering - Advice on some heavy duty patching/spackling

I recently moved into an apartment which I am subletting. The building management company seems to be very negligent, and I'm ready to undertake some of the fixing up myself. The walls look like they haven't been painted since the Clinton administration, so I plan on tackling this first. However, there are some serious trouble spots that I will need to address first. There are 2 rectangular areas where paint and a majority of the drywall is just missing. Both spots are perfectly rectangular. Not all of the drywall is gone, but a good portion of it is. A friend who is knowledgeable in this sort of matter told me that I should buy spackling and will probably have to apply a few layers and then smooth it over with fine sand paper. I'm not completely confident that this will remedy the situation, but he saw photos and seemed fairly confident.

Will this remedy the situation?

On a completely unrelated note, does anyone know if I have a chance of getting the management company to at least deduct the money I spend on spackling, paint and supplies from my rent? I've had landlords in the past offer this up as an option. Moreover, I don't think a tenant should have to pay anything additional just to have the place not look like a crack den. Any suggestions with this one?

Some pictures sure would help.

..... and spackling is just for minor repairs. Larger areas would need joint compound. You would have to come to an agreement with the landlord/management company prior to doing any work or spending any money before you could be assured that you will be reimbursed.

btw - welcome to the forums!
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