a) Bromine is an electron withdrawing group (EWG), which makes nearby protons more acidic. So the carbonyl with two bromines is the most acidic.
b) To perform alpha bromination, the enolate (or enol) must first be formed, which then attacks Br2.
The problem with doing this under basic conditions is that each successive bromination leads to a carbonyl that is more acidic, and so forms an enolate even more easily. So once this reaction starts, it's difficult to control.
Enols are less nucleophilic than enolates, so this react can be controlled under acidic conditions. (Br2/H3O+ instead of Br2/NaOH).