All of the three statements you presented—“This is paid for advertisement,” “This is a paid advertisement,” and “This is a paid ad”—are acceptable sentence constructions, if rather slipshod. I think their comparative appropriateness is not at issue and need not be discussed here.
Those sentences are not very natural-sounding though. I’d say that the more idiomatic, concise, and effortless way of saying them in any kind of media—print, radio, television, the web—is “This is paid advertising.”