What can I mix with Courvoisier?

Anything but water, basically. It's a great mixer for cocktails because it has a complex flavour that stands up to other ingredients well. Some popular options are the Courvoisier Manhattan (bourbon, sweet vermouth, and bitters) and the Courvoisier Sidecar (cognac, triple sec, and lemon juice).

Is Courvoisier a cognac or brandy?

Courvoisier is most definitely a cognac. It is made from grapes that are grown in the Cognac region of France and it must meet certain production requirements in order to be called a cognac. For example, Courvoisier must be distilled twice and aged for at least two years in oak barrels before it can be sold.