Sydney, Australia goes all out on the NYE fireworks, and with the time zones, it's one of the earliest.

Yes, but only the sex chromosomes - X or Y.
In other chromosomes, the genes effectively 'compete' for which one is encoded - that's where dominant vs recessive characteristics come from (eg your earlobes - in some people, the 'head side' is fully attached, but in most, it curves away and the lobe is a little dangly. 'Attached' gene is recessive to 'dangly').

The X chromosome is different. If it senses another X chromosome, one entire chromosome will shut down. Tortoiseshell cats are the go-to example here. Orange and black fur are X chromosome linked, so they have patches of orange or black fur depending on which chromosome has shut off. Extremely rarely, we see a male torti, but that's because they have XXY. I can't remember the exact deal of the Y chromosome, but I think it's that its genes 'enhance' existing programming rather than directly affect, so it doesn't matter if there's extra. Men who are XYY tend to be taller.

That said, most people who have trisomy X or Y only learn they do when they get help for reproduction issues, as it only really affects fertility. But past that, especially if it's extra X chromosomes, there tends to be developmental disorders.