When thinking about somatic variants and the allele frequencies of those variants it is important to consider the purity and heterogeneity (aka clonality) of the samples being sequenced. In cancer genome sequencing it is rare that a tumor sample is 100% pure (no normal cells) and is composed of identical tumor cells each containing the same mutations. Tumors change over time and a single tumor may contain multiple 'sub-clones'. Until we are sequencing DNA of individual cells we need to remember that we are sampling from a population of entities that are not guaranteed to be identical.

For the following discussion:

Variant allele frequency = read count supporting mutant base / total read count at that position

For heterozygous somatic variants we can expect a tumor variant allele frequency of 50% and a normal variant allele frequency of 0%. Of course there will always be some variability due to some of the technical artifacts already discussed (random sequencing errors, etc.).

Imagine you are identifying somatic variants in tumor DNA by comparison to normal DNA. The simplest case is where the tumor sample is pure (contains 0 contaminating normal cells) and is perfectly homogenous (all tumor cells contain exactly the same set of mutations). In this case, we should see a tumor variant allele frequency close to 50%.

Effect of poor tumor purity:

If the tumor sample contains contaminating normal cells, this will reduce the observed tumor variant allele frequency. Similarly, if the 'normal' sample was adjacent to the tumor it may contain some tumor cells and the observed normal variant allele frequency may be higher than 0%. Even if blood is used to obtain constitutive DNA for identifying somatic variation, it may still contain circulating tumor cells or cell free DNA that came from tumor cells.

Effect of complex tumor heterogeneity:

Even if a tumor is 'pure' with no contaminating normal cells/DNA we may still see somatic variants that have a tumor variant allele frequency of less than 50%. For example, imagine our tumor consists of a founder clone and a sub-clone derived from it. Perhaps the sub-clone comprises 40% of the cells in the overall tumor mass that we extracted and sequenced. In this case somatic variants that exist only in the sub-clone will have a substantially reduced tumor variant allele frequency.

When both purity and heterogeneity are in play, interpreting tumor variant allele frequencies just gets more and more complicated ...

Yes, generally you have the right idea, though some details change depending on how the sequencing was performed.

Clone libraries are created because each clone should only incorporate a single copy of whatever locus has been amplified. One then sequences some number of those clones. If you're working with a diploid organism then you can use a formula to calculate the probability that both copies of the locus have been sequenced for the number of clones you have picked. These can be extended to organisms with higher ploidy levels.

Somatic mutations could be picked up while sequencing, and their frequency in the output would correlate with how many cells in your sample carried that mutation. Although I don't do much of these analyses myself, I expect it would be very difficult to distinguish a somatic mutation from sequencing error. If you knew the error rate of your sequencing technique, and especially if you had a specific mutation you were looking for, detecting a somatic mutation should be easier. (There is also the problem of distinguishing between error caused by the sequencing machine vs. errors incorporated upstream such as contamination or a mutation while the DNA was in the clone.)

For the type of sequencing I do (Illumina) I would almost always classify a single read out of 25 as an error. As with anything, however, if you were very confident that your protocols and platforms reduced enough error, you may want to take a second look at the outlier.

As for over-representation of one chromosome or allele over another, it does happen and should be considered. However, I don't know much about these biases so can't say how dramatic they can be or which particular biases a specific platform is prone to.

I'd say in general, you should not expect one parental chromosome to be favored over another.

Depending on the techniques used, you might get some bias if one allele looks very different from the other, (say, because your PCR primers work better on one allele than the other) but in general, you should see each at about 50/50. If you get a very skewed difference, that suggests that you are looking at a false positive.

With most technology, a 1/25 mutation would not be distinguishable from noise. If you had 1000x coverage with high quality Illumina data, you could spot it. With sanger, never.

You can't have three alleles in the same organism, unelss there's been a genome duplication. You only have two copies of every gene, one from mom, and from dad.