1: The ocean is the only place where it's feasible. The continents have much, much thicker crust (40-70km) than the ocean basins (7-15km). Areas of exposed oceanic crust (e.g. Iceland) have much thicker than normal oceanic crust.
Beyond that, it's (slightly) easier to "drill" through water than through rock. There are a still a _lot_ of challenges involved in deep-water riser drilling. You don't just have a what's basically a steel rod going down (as you would with riserless drilling), you have to have a system that's capable of returning fluids and maintaining high pressure going all the way down to the seafloor (and below, once you case the well). However, it's still faster to deploy the riser than it is to drill through solid rock. At any rate, I'm getting sidetracked. The locations where they're looking to drill to the moho are in relatively shallow water (3-4 km) compared to the water depths that the Chikyu has already drilled in.
2: You're misunderstanding how drilling works. :) In some sense, what you've described is exactly how it works. (Just think of the drillbit as the robot.) However, you have to overcome the pressures at the depth you're drilling at (otherwise the hole will collapse, among other things) and you need an efficient way to return the cuttings (waste material) to the surface. Thus: drilling mud. You circulate pressurized (and very dense, so that the pressure increases with depth) fluid that flushes the cuttings back to the surface and keeps the borehole open. (It's an oversimplification, but that's the basic idea.) In some cases (e.g. coil tubing rigs), this fluid is even what drives the drillbit.
At any rate, hopefully that helps illuminate things a touch. :)