I wouldn't put it under cabinets just incase you want to change your flooring in the future. If you put it under the cabinets then you my find yourself removing the cabinets to remove the floor. Or doing a hack job cutting it out. Save yourself the future headache, no finished flooring under cabinets.

It's already from top to bottom. At this point would be marking the slab with a grease pen for crack length. Measure the crack width and mark the location of the measure with a grease pen as well. Check it in a year. If nothing moved, every 3 to 5 years.

PNW Engineer here... 3 things garenteed in life: death, taxes, and cracking concrete. You don't have a scale in your pictures, so the following is assuming some things.

That crack is nothing to be concerned about. It looks hairline. Monitor it, make some marks and measure it. If it's changing to where you can stick a finger it or your subfloor becomes uneven, then you have an issue.

As for the groundwater, it looks like you are in a corner of your building. Check your gutters. You may have a downspout too close to the foundation. In the winter here in the PNW, I add gutter spout extensions 6 to 10 feet away from the foundations. Check your surface grade to make sure no ponding is occuring. In the grand scale of things, this amount of water is trivial. If it starts to pond under the building, you can attempt to seal it from the exterior. It looks like a 3 foot crawl space, some digging and $20 in sealer. But if I were you, I wouldn't worry about it now.