The machine is capable of travelling to the end of the universe and back around through time, do you not think it can move itself up a few meters?
That's it. Everything else in the future hovers or is capable of movement, so the Time Machine is too. The Professor knows the dangers of phasing into solid matter so he would have built the Time Machine with the ability to move and a program to automatically do so to the nearest solid ground to its original location.
As for the flooded future, the Time Machine enters the normal time stream as a compact pocket of matter then instantly balloons to its original size, pushing any matter out of its way. This is easy to do with any matter near the gas or liquid phases but not in the solid phase which is why it can appear underwater but not in rock.
The 10-feet-above-the-air thing, when they crush their duplicates, has been discussed from here
, but essentially you either accept the literal explanation from The Professor (which contradicts the Time Machine's moving position) or you see it as a Paradox-Correcting action similar to in BBS (which the Professor calls it seconds later).