Well firstly you can answer the question without knowing about pcr! The way the disease is associated with one of the bands you see is all the information you needed to answer your question ‘which allele’. Well it seems you have done so. It is enough to enable you to answer the only question that comes up on your copy (rather badly worded) what is the probability that another son of this couple would have the disease?
For your not understanding about pcr markers, we here cannot really substitute for your textbooks and manuals, we mostly can only help clear up confusions you have from them. These often emerge when you are required to do an exercise like this.
However if it is a comfort I guess I agree you can say this is X-linked recessive. And your example is a relatively mild condition. You do have a homozygous affected female (relatively rare) who has been reproductively very successful and you also have an affected male who has reproduced. The affected males you could say literally are homozygous for one allele; males are always homozygous for X genes, I don't know whether geneticists say it that way.
For your question about pcr I don’t know whether your problem is with the ‘chemistry’ or with what the point of it is. To answer about e.g. why the lengths are what they are I would need to know more about the specific case, the genes and the primers, which is probably in your material.
But if the question is what is the point of microsatellites? It is that it if a gene had only one disease-causing mutation in a population then the conceptually simple idea of looking for it in screenings might also be practical. But if, as with haemophilia there are hundreds of different mutations known to cause the disease you need a different approach – you look at a family, and at what polymorphism is inherited along with the mutated gene by a relatively easy general method. A polymorphism of something near, or in a usually silent region actually inside the gene e.g. in an intron. These are e.g. microsatellites or short tandem repeats (STRs - the terminology tends to get somewhat rebarbative).
Pcr is a brilliant way discovered not that long ago to pick out and amplify so that you can see it, just one specific sequence of DNA out of all the vastly more rest of cellular DNA that is in a sample.
