Most genes are on the 22 "homologous" chromosomes, which you have 2 of. For those, you do have 2 copies of the gene (one per chromosome), one of which comes from the mother, one from the father—and which copy you get is effectively random (each parent does a process called "crossing over" that sort of mixes their two copies to produce the new chromosome they pass to the child). Punnett squares can be used for these genes.

That leaves the "sex" chromosomes, X and Y. Females have two X chromosomes and no Y, males have one X and one Y. (The Y chromosome is very small, has very few genes, and doesn't change much.) A mother passes down one X chromosome, via "crossing over", to a child of either sex. A father passes down either his full X chromosome, making the child a daughter, or his Y chromosome, making a son. (So, yes, it is impossible for a father to pass on X-linked conditions to his sons, while his daughters will always carry a copy. Meanwhile, if a male has an X-linked condition, then his mother must have at least one copy, so she's either a carrier or has the condition herself.)

I think most genes follow a dominant/recessive pattern, where AA and Aa behave the same (by convention the uppercase letter is used for the dominant allele) while "aa" behaves different. There are certainly exceptions to that, though. See https://en.wikipedia.org/wiki/Dominance_(genetics) (in particular "incomplete dominance", "codominance").

When you have one copy of a gene (usually because it's on the X chromosome—"X-linked"), if it is of the dominant/recessive pattern, then I would expect "A" to behave like "AA" and "a" to behave like "aa".

Note that, since crossing over never happens on the Y chromosome, it's passed down fully intact from father to son, and the only changes that can happen to it are mutations—a very slow process, compared to the mixing that occurs on the other chromosomes. Evolution on the Y is thus rather slow. Also, (according to Wiki) the Y is estimated to have only 63 protein-coding genes, while the X has 804. I think the Y mostly just serves to make the child male.

This is a helpful, detailed explanation. Thank you!