> how does the „two copies“ phenomenon of the human genome and the „two copies“ thing of chromosomes fit together? Are those one and the same concept?

Which phenomena are you referring to exactly? That we have two copies of each chromosome and if they mean we have two copies of the human genome?

> Are there two copies of the XY chromosome, too?

Each of our non-sex cells[1] contain two sex chromosomes: one from our father and one from our mother. Since your mother always inherits her X chromosome, your sex is determined by which sex chromosome you got from your father. If you are a female (XX), your father passed on his X chromosome. If you are a male (XY), your father passed on his Y chromosome.

This rule makes for some interesting inferences. For example, your father in turn got his X chromosome from your grandmother and his Y chromosome from your grandfather (both on your father side, of course). Your mother, on the other hand, got his X chromsome from both your grandparents on her side.

So if you're a male, your Y chromosome was passed on from your grandfather on your father's side. If you're a female, one of your X chromosome comes from your grandmother on father's side, but your other X chromosome may come from either of your grandparents on your mother's side.

You can trace this Y-chromosome lineage back to what's called the Y-Chromosomal Adam, which is the last universal common ancestor of all currently living human males[2]. You can make a similar inference using your mitochondrial genome[3] and arrive at what we call the Mitochondrial Eve[4].

Our sex cells[5] are different, since they only have one copy of our chromosome set. The number of the chromosome set we have is called ploidy[6] and so our sex cells are haploid cells, as opposed to our non-sex cells, which are called diploid.

If you're a male, a single mature sperm cell in your body contains either the X or Y chromosome. For females it's different, since they only have the X chromosome, all their mature cells contain only one copy of the X chromosome.

[1] https://en.wikipedia.org/wiki/Somatic_cell

[2] https://en.wikipedia.org/wiki/Y-chromosomal_Adam

[3] https://en.wikipedia.org/wiki/Mitochondrial_DNA

[4] https://en.wikipedia.org/wiki/Mitochondrial_Eve

[5] https://en.wikipedia.org/wiki/Gamete

[6] https://en.wikipedia.org/wiki/Ploidy