"Do you have a ticket to this show?"
Translation:У тебя есть билет на этот спектакль?
есть is used when possession is the important factor. You would drop it if you used an adjective.
For example, in у меня есть яблоко (I have an apple), the fact that you have an apple is the important piece of information. However, if i were to say у меня большое яблоко (i have a big apple), есть is dropped because we have an adjective, making the fact that your apple is big more important than the mere fact that you have an apple, if that makes any sense.
No. At its core, есть means "to exist", and appears is other formats where it doesn't mean possession. The format "у [person/thing: Genitive case] есть [thing: Nominative case]" usually means "[person/thing] has [thing]", but it's a very idiomatic translation.
For example: "Справа от гостиницы есть хороший ресторан" means "To the right of the hotel there exists/is a good restaurant".
If you mean "У тебя есть билет для этого спектакля?" it's grammaticly correct and you would be understood, but we just don't say that way. Only билет на спектакль, билет на концерт, билет на футбольный матч. Or with transport: билет на поезд, на самолёт. But unexectedly: билет В кино, билет в музей. Why is that? I don't know actually:) I'm afraid you should just memorize it.