Is a sebaceous cyst painful? Is it something that just stays there forever?

Usually painless... ...Unless getting infected which happens and should be operated on if no response to antibiotics or if antibiotics help, should be excised later.
Can be. A sebaceous cyst is simply a cyst filled with oil. They can be painful if they get large enough or if they become infected and turn into an abscess. They can be removed, depending on the size and location, by an in office procedure. They do not become cancerous so no risk to just leave it alone.