is they're probably aesthetic - house isn't going to fall down, they're just ugly.
To check up on the guy fixing the insulation:
The key element in dealing with condensation in your ceilings (and walls) is the vapor barrier. It's a sheet of plastic-like material that keeps the water vapor on the "warm" side so it can't reach the cold air and condense. If you're in a temperate climate, it should be under the drywall, in front of the insulation. (If you're in a very warm climate - think Miami - then it'll be on the opposite side of the insulation. I'm gonna treat the rest of this as if you're not in such a warm climate)
It was either a very large roll of material that was stapled in place before the drywall was installed, or it is the paper-like facing on the warm side of fiberglass bats. You should not have such material on the "cold" side (attic side). The attic side should just have "raw" insulation. There also should not be a vapor barrier in the middle of the insulation. (often people will add faced bats when upgrading their insulation, which is wrong. Need to use unfaced in that situation.)
The cracks themselves:
The cracks are probably happening because the people who installed your drywall did not properly account for expansion of the drywall as it heats up. They should have left a small gap between the panels so that they have room to expand - the panels expand with heat, and if they're too close the only way they can expand is into the room, creating a crack.
To fix this, you can create room for that expansion. Use a utility knife, router or other convenient cutting tool to trim the drywall where it is cracked so there's room for expansion. The gap should be something like 1/8th of an inch or a tad larger. Don't go bigger than a 1/4 inch, because that will make it harder to finish the drywall. Then you'll need to apply drywall tape and drywall compound to cover up the gap. It's easy to do, and there's lots of resources on the web describing how.
The microwave condensation is probably being caused by the range vent in the microwave. There should be a small door inside the vent that prevents the cold outside air from reaching the microwave. That door might be stuck. The "easy thing to try" is to use something like a shop-vac or other vacuum to try and clean out the vent from the outside. Beyond that the fixes start to heavily depend on how exactly the microwave is installed and vented, and your abilities with tools.
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