On evolution statistics
In your 5 points you basically cover several concepts of evolutionary biology.

1) The number of mutations depend on mutation rate. The mutation rate varies along genome sequences, species and individuals. According to the recent DECODE study (Kong et al., 2012) a human mother transmit on average 15 mutations to her offspring and a human father transmit on average $25 + 2(g-20)$ mutations to his offsprings, where $g$ is the age of the father and where the formula stands only for father older than 20 years old.

2) Mutations happen by chance and are not directed toward creating some specific feature. But it is much more likely to create a round of color on the wings of a butterfly than creating the picture of Tom Sellek. The reason has to do with the developmental and biochemical pathways linking the given mutation to its phenotypic effect. Looking at a given mutation, you can understand how it yield to the modification of some phenotypic trait by looking at the biochemical and devlopmental pathways.

3,4) The third point that you raise is called "genetic drift". Shortly speaking the concept of genetic drift may be called the good luck/bad luck effects. Stating differently genetic drift is the random sampling of alleles (gene variant) from a population. If some alleles are favored over some others at a given locus, then sampling is not 100% random but is not either 100% deterministic. The only case where genetic drift is absent is in infinite population (which is obviously an unrealistic case). Genetic drift is inversely propotional to population size and you'll understand it better by reading this post.

5) When the mutation is at very low frequency, the mutation needs to be dominant in order to be expressed, this is true. But an allele may increase in frequency due to genetic drift up to the point that some individuals are homozygous for this allele and therefore express the trait. Dominance and recessivity are just extreme case of a continuum and most often alleles have intermediate level of dominance. Pleiotropy is also something to consider. Note also thaat the frequency of the three possible genotypes $AA$, $AB$ and $BB$ are given by Hardy-Weinberg law (under some assumptions) $x^2$, $2x(1-x)$ and $(1-x)^2$ respectively, where $x$ is the frequency of the allele $A$.

Hope that helps!