If you are wondering where all those stray edges came from, its when you used intersect faces with model. This made everything you selected intersect with everything else and form an edge wherever they came together.
It takes bit of time to get your head around the three intersect with options, but I assure you they do many sense (in about your 5th year of using them).
It is all about understanding ‘context’.
If you have two raw geometry faces intersecting, they are in the ‘same Context’ and as such when you intersect them the edges will join them and become part of the their geometry.
But if you have 2 cubes that are grouped separately, each has its own ‘Context’ and they are both in another ‘context’. So if you select those 2 groups and use intersect with model the edges will form wherever they meet, but the edges will be formed in the current ‘context’ which is outside both of the groups ‘contexts’. So you end up with the 2 original cubes and a bunch of stray edges.
But, if you open one group for editing, then select its geometry and choose intersect faces with model, you are now in the cubes ‘context’ and the edges will form within, allowing those edges to interact with the cube geometry. The other cube, being outside the current ‘context’ remains unaffected, and no edges form outside the context of the edited cube.
This probably sounds more convoluted than it should but it is often difficult to explain something that is really simple, but only once you understand it.