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Using indicative or subjunctive implies ideas, only exceptionally style.
In your list of examples the last is the only one that admits both moods and some consideration about style is appropriate. The educated manner is trying to avoid any appearance of one looking for some specific answer if you really don't mean that, besides it is considered stylish to hide our own expectations and feelings. Some questions call for an affirmative answer by using indicative, some others call for a negative one by using subjunctive. The safest way is using subjunctive because you can safely communicate -by intonation and wording- that you are not expecting a negative answer.
¿Crees que la fiesta va a empezar pronto? (we don't know but it looks like we're expecting so)
¿Crees que la fiesta vaya a comenzar pronto? (we're not expecting so / we don't know and we'd like to)
Tú crees que la fiesta es hoy. (that's what you think ---> believed )
Tú no crees que la fiesta sea hoy. (that's what you think ---> not believed)
Tú no crees que la fiesta es hoy. (what you think opposes to what I know for sure)
Nosotros dudamos que la fiesta sea hoy
Nosotros no dudamos que la fiesta sea hoy
Nosotros no dudamos que la fiesta es hoy
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