@MrsWinslow - You have the right idea. Homologous chromosomes under mitosis for regular old cell division, like when an embryo is growing--each new cell with have all the same chromosomes. But a gamete (egg or sperm) will have just half. That's why two people could have a pretty infinite number of different children, because there are so many different possible combinations of chromosomes.
Y definitely has no match and it's a very small chromosome that doesn't do much besides make a boy. In women, there are two X chromosomes, so I guess they would be homologous, while in a man, there's just one, so it has no match. That's why men are more likely to be colorblind. The gene for this is located on the X chromosome.