The reason why something is made more acidic, is because its electron density is being removed to another part of the molecule. Keep in mind the difference between inductive effects (the ability of a group to pull electron density toward it through the sigma-framework), and resonance effects (the ability to draw structures with the pi-electrons redistributed). Both can "pull electron density around a molecule", but in general the resonance effects tend to be stronger.
First, consider the inductive effects only. Generally they're easier to consider because you don't have to redraw anything, you just need to have two groups connected by bonds. Different groups have different abilities to "push" (+I) or "pull" (-I) electrons. You should have a table in your book which ranks the order of various common groups. Check how the inductive power of bromo- and nitro- compare. Does this explain the observed effect?
Secondly, consider resonance effects. If you can draw a resonance structure which removes an electron pair from substituent A, and adds and electron pair to substituent B, you can say that B has removed electron density from A. Is either bromo- or nitro- capable of removing electron density from the aniline nitrogen?
Things can get more complex when the inductive effect of a group is opposite to its resonance effect (e.g: methoxy- is sigma-withdrawing, but pi-donating). When considering these cases, check to see if the two groups you are considering are in conjugation. If they are, the resonance effect almost always wins, if they are not in conjugation, the inductive effect almost always wins.
This brings us to your second question. Again, consider the inductive and resonance effects. In this case, the only difference is the location of the nitro group relative to the aniline. How would location effect inductive effects, and how would it effect resonance effects? How would these various effects stack?