I really don't think a monk with a full BAB would be underpowered.
The fighter gets a feat every level. A full BAB monk would end up getting more than a fighter at times. Granted, it would be like building a fighter with preselected feats/abilities most of the time, but you'd have a lot of extra stuff to make up for it.
Sort of. I'm very used to core only play, So I'm coming from that perspective. With Archetypes and the expanded monk weapons list I'll admit it might get crazy.
Full BAB would drag the Monk from the very bottom of the pile and put him ahead of the Rogue IMO. The Monk bonus feats are not that great, their weapon proficiency's stink, they have a D8 hit die, fewer skill points than the Ranger and it's not like slow fall compares to favoured enemy, weapon training or the immense host of paladin abilities.
Also, even with full BAB they would still be the most MAD class there is.