Yes you can set drywall directly to the block wall. If it intersects with an exterior wall that is exposed to the weather, I would place a layer of poly of out of the intersecting corner, if accessible, out no more than 2', 18" would probably be better, vertically to prevent any moisture coming through the block and getting into the sheetrock. Use drywall clips to hold the corner, so no nails go through the plastic. If it does not, ignore this recommendation.
To mount the drywall use a glue in the large tubes, you will go through a lot. Blob on golf ball sized portions of glue on an approx. 16"X16" grid. Set your drywall onto that and secure directly into the block with drywall nails. that is if they pass the test.
To test your nails drive a few drywall nails into the face of the block before you start your drywall install. Do not nail in the joints, the mortar is much denser. On true cinder block, not slag block, (slag block is a newer process ) I have run 1 1/4" drywall screws right into the block, that may do what you need right away. Other nails to try just to hold the sheetrock long enough for the glue to grip are roofing nails. Find one of theses that is suitable for your install.
After you sort out which fasteners to use, hold the sheetrock tight to the wall in the place you want to nail or screw. Set your fastener, some help here would be beneficial and set a few more before you move down the sheet to add more. The amount of fasteners needed will be only enough to hold the sheet flat, the glue will do the rest.
There's almost always an inch or two of space behind dishwashers. There isn't a standard depth, so the cabinets aren't built for that exact dimension.
It's usually fairly simple to pull dishwashers--two screws at the top or sides of the cabinet faceframe. Flooring set in front can make it challenging, though.
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You should have them come back, remove the valve, and install an elbow and a short nipple so the valve is outside the wall (make sure it's out far enough so that it's outside the finished wall). Then have them install the valve again.
If you know what you're doing, you could do the work yourself, but I don't recommend it.
Unfortunately the pipe bends the wrong way after the last elbow, otherwise you might be able to give it a quarter turn so that the elbow pointed out into the room. In your situation, however, this would loosen the joint, so it's not recommended.