Hmm, I always assumed that the line reads as "Dodge, Improved Unarmed Strike, (base attack bonus +2 or monk level 1st)" so you need BAB +2 or 1st level Monk. However I see that it could be read as "(Dodge, Improved Unarmed Strike, base attack bonus +2) or monk level 1st", but honestly I doubt it.
If you then look at Crane Wing for example:
Prerequisites: Crane Style, Dodge, Improved Unarmed Strike, base attack bonus +5 or monk level 5th.
If it was the second interpretation, that would mean that a Monk level 5 wouldn't need Crane Style to pick Crane Wing, which makes no sense.
So in other words, yes a monk needs Dodge, unless he somehow picks it via his bonus feats (Master of Many Styles for example), which ignore all prereqs.
Didn't you already ask this a few days ago? The answer is still yes. You need to meet all of the prerequisites. One of them is bab +2 or 1st-level monk, not just being a 1st-level monk. The only way to get rid of Dodge as a prerequisite is to be a Master of Many Styles. The bonus feats they get let you ignore prerequisites (with a few limitations).
Yes you have to meet the other prerequisites. Notice the placement of the comma.
Each prereq is seperate from the others. The only two in the same listing are the monk level and BAB bonus so they can replace each other. The monk level does not replace everything else however.