Hi Lucy 😆 In this sentence “on” doesn’t just function as a preposition like it normally does. That’s because in English, when talking about shows or movies, “is on” is an idiomatic phrase which means “is broadcast/transmitted/shown.” If “on” were removed we wouldn’t know what the state of the program is or what is happening. Here’s another good sentence: “Come quickly! Our favorite series is on! (Being shown now)”

Yes, the sentence would still be valid, but not very good. The problem with the sentence "This program is twice a week" is that "is" here is an imprecise verb. It doesn't really say what you want to say. Better verbs would be: "This program PLAYS twice a week" "This program RUNS twice a week" "This program HAPPENS twice a week"