Gosh... You don't need to understand DNA and all that. Chill... I believe your doctors are on top of their game.
Your list is basically correct, with one small comment: I think that you are mixing up the 2 DNA strands with the 2 alleles (when you mention "A-A" and "A-C" - those are the nucleotides in the strands). Since we inherited 2 copies of each chromossome, we have 2 pairs of strands, and each pair is an allele, one that came from our mother and one from our father. In some texts you may see alleles described as "possible variations" (as in "there are 5 alleles for this gene"), but although correct I think it only adds confusion to the matter: think of alleles as the 2 gene versions that we got from our parents.
To keep it simple, let's consider that one gene equals one protein (this is true for simple and small proteins, but there are many exceptions to this over-simplification and one protein may require several genes, or a combination of X genes may generate Y proteins... Forget this for now). So, whenever a cell needs to produce a particular protein (and proteins are the basic components for everything in our cells), it needs to go "read" the "recipe" for assembling that protein, and that recipe is written in the gene sequence within the long DNA. A protein is a linear chain of smaller building blocks called aminoacids, of which there are only 20-something different possibilities. The exact sequence of aminoacids is crucial for the protein shape and its shape determines its function: so, if a protein needs a block called "valine" in position 34, and for some reason the sequence in the gene for position 34 says "proline" and not "valine", then the assembled protein is incorrect and that protein may not work as well or not work at all. That is non-problematic if that error occurs, for example, only in the father-allele and the mother-allele is correct and stipulates "valine" in position 34. Worst case scenario, the cell is only able to produce 50% of functioning proteins, but that may be more than enough or can be compensated by increasing the production rate of that protein. But it may also happen that the non-functioning protein interacts with the correct protein, or creates some unforeseen problem instead of being just junk floating inside the cell. Or in many cases one of the parental copies is permanently disabled, and it may happen that the cell disabled the correct version and kept active the wrong one... Then we have a problem that may be the cause of a genetic disease.
Now, there is something very close to the concept of "allele" and that is a "SNP". Usually (but not necessarily) "allele" refers to equally correct versions of a gene (for example, one allele stipulates "brown eye" and the other "blue eye"; in this case none of the alleles is wrong, but because some alleles are stronger (dominant), brown-blue results in brown eyes and only blue-blue permits blue eyes). Alleles are functional entities - it does not matter if the "blue eyes allele" is actually 1 or 5 genes. On the other hand, SNPs are identified variations in the sequence of a gene (in the example above, if it is known that 5% of the population carries a gene version that states "proline" in position 34, that variant is a SNP). This is important, because once SNPs are described and their natural occurrence is known, it is very easy to search for them in a genetic analysis: you search for the 95% SNP and the 5% SNP, and one of them should be found. If none of them is found, then the geneticist needs to sequence the genome and identify the novel SNP for future studies. In MOST cases, SNPs are benign: they don't even affect the protein activity. But there are many cases in which a particular disease can be linked to one single SNP.
Did it help?