If i start a minecraft server and am not online can other people still be on my server?

Yes you can! There's a problem when you go one your server I don't suggest you op your self because if anyone comes on the server when you not on with the offline account they get op.

Depends what kind of server it is. If you're hosting it on your computer (you download a server from the Minecraft website) then the server must be running and your computer must be on for others to join. But if you are hosted by a website like BeastNode (my favorite) then your server runs 24/7. Unfortuantely 24/7 servers cost money each month