Saturn's ocean moon, Enceladus, is attracting increasing attention in the search for life in our solar system. Most of what we know about Enceladus and its ice-covered ocean comes from the Cassini mission. Cassini ended its exploration of the Saturn system in 2017, but scientists are still working through its data.
Too heavy. :p
Drilling slowly through ice with heat isn’t a very spectacular claim, at any rate. You’d need to keep the descending arm heated too I suppose, otherwise it’d all get stuck as it refroze behind the drilling area. But the sheer distance is the only potentially currently impossible hurdle, off the top of my head. Gravity is providing all the force you need, no motors should be needed. Use a radioactive, low output heat source. You’re not in a hurry or anything.