Can you get married without saying vows?
Yes you can, it's commonly known as a justice of the peace wedding. It requires the bride and groom and a couple of witnesses. You don't have to recite vows if you don't want to.
What is it called when you get married without telling anyone?
Eloping means to get married without telling anyone, especially your parents. To elope may also suggest that you forgo a formal wedding and elope for the ceremony instead.
Can you get married without the other person being there?
A proxy wedding or proxy marriage is a wedding in which one or both of the individuals being united are not physically present, usually being represented instead by other persons. Proxy weddings are not recognized as legally binding in most jurisdictions: both parties must be present.