Yes, you could and yes, you can :D "No more" is equivalent to "anymore" and "any longer." Only the sentence structure changes when you change these expressions. You use "any more/longer" with a negative sentence and "no more/longer" with an affirmative sentence. "Your card is not valid any longer." "Your card is not valid anymore." "Your card is no longer valid." "Your card is valid no more." All these expressions mean the same thing. (The last one just sounds a bit dramatic and outdated for modern spoken English)

It's hard to put into words, but no more is for when you run out of something. For example: There are no more cookies. But like you said longer relates more to time. Ex: I no longer have any cookies. Hope this helps!