‘Over’ in what sense? ‘Ended’? ‘Across from above’? ‘No longer affected by’?
Across, on the far side
It can be used in all the ways you have suggested above.
Are "ar draws" (learnt in the Gwledydd lesson) and "dros" (leanrt in this lesson of directions) the same meaning of "across"? Would you "yn dros y cefnfor" for example, instead of using ar draws for a change?
Yes, more or less, but yn is not used with dros.
during? dros penwythnos: over or during the weekend
Is this the mutated form of "Tros", if so why is it mutated?
Yes. Over the years it has become an alternative form of tros in nearly all situations.