The best way to tell if your reaction is complete is by TLC, following the disappearance of your starting material. Unless, of course, you have access to some really nice instrumentation like HPLC-MS or GC-MS. This reaction is usually so much slower than addition across an alkene that following the disappearance of the red color isn't as useful as it is in that reaction. Bromine has a high enough vapor pressure that it will evaporate out of the reaction mixture if you leave it there long enough.
Bromine is much more selective than chlorine, and since the transition state is very late in the reaction pathway, the stability of the alkyl radical determines where in the compound it will react. However, if there are two sites on the molecule that have equivalent radical stabilities, you will still get statistical mixtures of mono-, di-, and non-brominated compounds (assuming 1 equivalent of bromine is used).