Look at the table of half reaction potentials. In both solutions you have redox systems, the question is what direction the reaction can take - will something change, or not. Potentials will tell you the answer.

http://www.google.com/search?rls=en&q=half+reaction+potentials

In case you are not familiar with these: half reaction potential is measurement of oxidation/reduction "strength". Comparing potentials you can check what will happen when you mix redox reagents.

For example - noble metals dissolved in ionic form are replaced in the solution by the least noble metals (iron fillings cover with copper if put into the Cu²⁺ solution - sopper is reduced, iron is oxidised). To check which metal is more noble and which is less noble, you can consult half potentials table.

In this partcular case the answers are pretty obvious (no intention of offending you).

First - bromine and iodides. It is in periodic table - which one of these elements is more reactive? Which is more likely to be in the free form, and which in the reduced (anionic) form?

Second - magnesium and lead. Which is more reactive?

Half reaction potentials are the most general way of dealing with such questions, that's why I referred to them. I have no idea at what level you are learning chemistry, if it is not in your book - perhaps that's all before you

first you have to determine what the compounds will do in an aqueous solution, by this i mean: ask yourself whether or not these compounds will split up in ions or not.... (this should be in your chemistry book under PRECIPITATION reactions and solubility of salts in water)
so, now you know what compounds are formed, you can do your REDOX reaction

How is it going to work for prediction of the first reaction - bromine added to iodides solution?

What in case of bromine added to chlorides solution?

I have nothing against simple approaches - if they work.