All concrete cracks to some extent. While cracking is unavoidable, you can control where and how those cracks develop. This is where joints come into play. Both expansion joints and control joints are critical to concrete flatwork, but each type serves a different purpose. Expansion joints are designed to allow an entire slab to expand and contract without coming into contact with an adjacent slab, wall or structure. As you noted, a good place for an expansion joint or expansion material would have been around the electrical boxes and between slabs. Control joints are used to relieve the stress within a concrete slab. These joints, which may be formed with a jointer before the concrete sets or cut with a saw after the concrete hardens, are designed to "control" where the crack will occur by inducing the concrete to crack in the location of the joint. The placement and number of these joints are critical. (See Be Active in Deciding Where Control Joints Will Be Placed). It appears from your photos that the floors are saw cut in a square or tile grid pattern. If so, there seem to be plenty of control joints present, meaning the issue is not a lack of control joints, but rather their location in the slab.
Regarding your question of what number of cracks is considered acceptable, there are no hard-and-fast standards that I'm aware of. In all the cases I've been involved with, it comes down to floor size, perception and safety. On a floor comprised of thousands or tens of thousands of square feet of concrete flatwork, a few cracks are to be expected and are generally deemed acceptable. When the number becomes unacceptable is the gray area. Non-structural surface cracks are not as critical and pose only an aesthetic issue, so they are usually tolerated in larger numbers than structural cracks. The cracks in your floor appear to be structural, running through the depth of the slab and starting to come apart in certain areas. Aside from the number of cracks, their severity leads me to believe they are beyond what I would consider acceptable for a floor of this type.
Methods for stopping the formation of additional cracks are limited. If the subbase is jeopardized or was not prepared properly, no number of control joints will limit the cracking. It will continue to occur until the slab has come into equilibrium with the base on which it rests and the stress causing the cracks has been alleviated. Sawing additional control joints in places where there may not be enough of them is about the only solution. Consider having a concrete engineer inspect the floor and determine if additional joints are warranted and where they should be placed.
There are a number of remedies for repairing cracks in concrete floors. The technology has come a long way in terms of crack repair polymers and injection systems. Today, you can inject cracks with a resin (epoxy, polyurethane or polyurea) that will actually attain a strength greater than most typical concrete slabs (see Epoxies vs. Polyurethanes for Crack Repair). This means that the repaired crack will actually be stronger than the surrounding area. These repair systems are usually injected into the crack after cleaning and crack chasing (routing out the crack with a saw or angle grinder), and they cure in 12 to 24 hours. Some color choices are available, but aesthetics are usually not the most important factor. Another option is to fill the cracks with a concrete caulk, which is usually made of a softer resin material. These products are applied to the crack or joint with a caulk gun and are available in a wide range of colors. Because this type of repair is more visible than crack injection, aesthetics are very important. (For sources, visit Concrete Repair Products.)
I suggest that you start monitoring some of the cracks in the floors to see if they continue to move or remain static. If they are still moving or growing in length or width, crack injection may be the best solution. If they are static, a crack filler is best. The crumbling pieces of concrete may need to be removed, or they can be glued back into place with either system, depending on the size and depth of the pieces.
In the areas of the floor where you say "the cream is popping off," this is likely to be spalling or scaling. On interior concrete slabs, this is usually caused by overfinishing or excess water in the concrete, resulting in a weak surface. The cracking is probably causing an already weak surface to come off.
I believe that the cracks in your floor are caused by poor subbase preparation or some major movement or deficiency under the slab. If the proper amount of reinforcement was used, the concrete should hold together, despite the cracks, and not separate or heave. Ask your builder to provide documents showing how the subbase was prepared, the type of concrete poured, slab thickness, and the amount and type of metal reinforcement. I think you have a pretty strong case that installation deficiencies caused the problems with your floors. The fact that the contractor who installed the concrete is out of business also does not give me a lot of confidence in the quality of the work.
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