I'm worried about people seeing my private videos. Can I keep videos private?

Yes. You don't have to make your videos public. When you upload your video you can choose the type of accessibility - public or private only. Videos marked "Private" will be available only to people whom you are calling friends. The lists of your friends and people who call you their friends (you can watch their friends only videos) can be found on "My Account" and "My Friends" pages when you are logged in.