Yes, the function of both toggle switches is the same. But do note that the revoiced Doom 2s have a
higher crossover frequency than the original version.
No, you've got it backward

The up position is a low-passed clean blend that also filters out high frequencies above the crossover filter and the down position is a full-spectrum clean blend. In both positions the "bass" pot functions as a clean volume control, but the "x-over" toggle switch determines whether that clean volume is low-passed or full spectrum; think of it as "up" means the crossover is engaged and "down" means the crossover is disengaged.
The newer (more laconic) labeling is a somewhat nebulous because it can easily be read as "up" is no effect and "down" is "x-over." This propensity toward ambiguity also extends to the nomenclature of the EQ: it's not hard to use in practice, but it is a curious architecture and its labels are misleading—or, to be more generous, counterintuitive—because they suggest a 3-band EQ when in fact the "bass" is a clean blend, the "mid" is a midrange boost/cut control as you'd expect (and therefore even more confusing given its functionality is not paralleled by the "bass" and "treble" pots), and the "treble" is a 2-pole resonant LPF. My best guess for why the treble pot is an LPF is Spencer was inspired by gated fuzz pedals which have often been used for bass synth (the Iron Ether Oxide is an example of this sort of design and function).