Solid Hardwood, Engineered and Laminate Flooring - Broken Subfloor

Here's my situation:
I am replacing all of the flooring in the lower half of my apartment. I plan on putting in kitchen tile and making the rest of the floor laminate wood. I have most of this planned out, but there are a few details I want to make sure of.

To begin, I live in a co-op, so I can make most changes as I choose. But the organization is responsible for the building structure and exterior. The apartments themselves are ~40 years old. My space is a 2-story, shaped like stacked shoeboxes. My enclosed (with interior window) kitchen, front hall, closet, and stairs are in the front 1/3rd of the first floor. The back 2/3rds is an open space w/ a 1/2 bath under the stairs.

I have already cleared away all of the flooring downstairs except the kitchen linoleum. Underneath is nice, pretreated 5/8ths plywood. I have cleaned this and removed all nails, carpet boards, etc.so it is nice and smooth. The problems though are two:

1. The remainder of a rotted hole (about 8" in width) is in front of the sliding door in back. I plan on replacing this 4'x8' plywood board with a new one as it perfectly spans over the entire length of the sliding doorframe. (which I plan to replace later) The real problem though is the end of the joist inside the hole. My bottom floor actually has a level below it belonging to the Complex. (it's built half in a hill). Could this even be repaired, if I manage to convince the Complex? Wouldn't that potentially screw up my level flooring?

2. The apartment is actually one of four in a row. Mine is one of the center two. When they laid the plywood downstairs (and prresumably upstairs) in my apartment they built it all as one structure. So the plywood subfloor on both sides of the apartment extends into both of my neighbors'. Here is the problem: while the vast majority of the floor is level, it does sage 1/2 or so the 1-2 feet near the side walls. I'm guessing this is simply due to the age of the building and how the main walls are supported below. My plan is to use either levelling compound or possibly shingles around these edges. Would the leveling compound cause a problem for my neighbors though? And I'm not sure if the shingles will even work. What do you think is the best option?

I plan to use laminate flooring in the main room, 1/2 bath, front closet, front hall, and maybe even up the stairs. So there are potentially lots of nooks and crannies along the side walls. Any suggestions? Am I missing something?

Make sure you fix has strength built into it, and not just a bandaid.

Self levelers are not DIY friendly!!!! Make sure your structure can handle the extra weight that self leveler adds. Self leveler is not for spot repair, it is meant to be poured over the entire floor to bring it up at least a 1/4" self leveler will not feather edge, so it must be damed up to limit flow. Self levelers have a lot of moisture in the mix, and could take weeks to dehydrate enough for your flooring to be laid on top. Shingles or even sand can be a better solution.

I was thinking a second joist could be laid either on one side or both.

If leveler really is a pain and heavy (dangerous) than I definitely will use the shingles.

Thanks.