Both words are quite common as far as I'm aware. I would use the word prejudice more frequently in its adjective form - prejudiced. If someone is showing bias or preferences for one thing over another without any good reason, you might call them prejudiced. It's a fairly negative word. You might also use this word to indicate someone is being racist, sexist or discriminatory but you would prefer not to use such as strong word. To jeopardise something means to deliberately or accidentally make a plan fail. Maybe you don't want to see someone else succeed so you might jeopardise their work. Again, pretty negative word but definitely a word that I'm familiar with and have used.

Jeopardize is US spelling, Jeopardise is UK spelling. Both jeopardise/jeopardize and prejudice are standard English words and you will find them commonly spoken in any English speaking country. I'm Australian/Canadian and my partner is Canadian.

Yes, both are common words. The word "prejudice" is particularly common in the US, where there is a great deal of discussion (in politics, but also in everyday conversations, both online and in person) about the problem of widespread prejudice against particular races, ethnic groups, religious groups, sexual orientations, etc.