My mom bought a house in 2018 from flippers that we have come to discover did not know what they were doing. Other than a laundry list of other issues one think that has been bothering me for awhile is a set of kitchen cabinets (see pictures).

The gaps between the walls/ceiling has been growing so I advised her to take everything out of them while I research how to best correctly install them. 

These cabinets appear to be held up by 6 screws in the leftmost cabinet (1 in each corner and 2 on the top) and 4 in the rightmost cabinet (1 in each corner, none on the top). Not shown verry well in the pictures is that I can see one of the screws has already come out of the wall in the gap on the back. It is likely that the top corner screws (and the 2 top in the leftmost cabinet) have already begun to let go based on the shape of the gap/leaning of the cabinets.

This house has very thick plaster walls, like 1.5" - 2" thick. I am currently planning on taking these cabinets down and evaluating how much damage was done to the walls and then attempting to reinstall these with proper length screws and anchors. This is a semi permanent solution (doesn't have to be perfect) as we plan to renovate the kitchen in the future (may be a few years).

Does anyone have any advice about:

1) How to properly mount cabinets (screw placement/mounting system)?

2) How to properly mount them in thick plaster walls?

3) Any way to tell if I might hit any electrical or vents (we believe there are some behind the cabinets)?

4) Is it worth trying to correct this by reinstalling or should I build a supporting frame for them to rest on that puts the load on the counter/cabinets below them?

5) How best to make these more weight bearing (if possible)? This may come with proper installation but my mom does have a lot of heavy dishes that go in these cabinets so it would need to be able to support that. 

6) Anything that I am missing with this kind of work? I am trying to grow my skills and am open to learning!

(Thank you all!)
 

Advice on correcting shotty kitchen cabinets