"If there is drainage, especially of subglacial lakes near coastel areas, there ought to be open cavities, since the water is following the lowest topography."
1)once a cavern has drained and no more water is coming in or being generated, it will close thru ice creep and macroscopic motion in roughly
t= (linear dimension of lake)/ (ice flow velocity)
this is seen in greenland for example, the conduits draining a melt lake usually do not persist into the next year, in some cases close faster, melt lakes appear at new locations, which sculpt new conduits und so weiter.
2) As i remarked in another thread, subglacial water can flow uphill. Off the top of my head, the ice-water interface slope is about 10 times the ice-air interface slope, and in the opposite direction. So if you have a horizontal bed with a little hole in it fulla water, and the ice air surface above the hole slopes down in the downstream (ice flow) direction, the surface of the water in the hole slopes up 10 times as much in the downstream direction. So the downstream side of the hole has to higher than the upstream side to confine the water. One can work out that in the case of retrograde bed (slopes downward upstream) that the slope has to be 10 times the ice air slope in downstream direction to confine water beneath.
Please do work the pressure/angle relations out yourself, I am quoting from memory, as always, I could be wrong.