Hmm...don't quote me on the first one, but I'm pretty sure you would use the bi- and tri- prefixes since both are nonmetals.
The second one, CuMnO4 is Copper (I) Permanganate. MnO4 is the polyatomic ion with a charge of -1, so Copper must have a charge of -1 to balance that out.
The arsenic one I have no idea.
And finally, the O2 molecule is usually just referred to as oxygen gas unless it is part of a larger compound.
Hope this helps!