I've been searching for some time now if this is always the case, but google gives me no easy answers. Infact, it doesn't even seem to know what prepositional objects are.
In every german sentence I see, the preposition is combined with some noun to form a prepositional object and then used in a sentence. Is this an always true thing?
Your terminology is mixed up.
Wir warten auf den Bus.
That part auf den Bus is a prepositional object. Same as in the English phrase We wait for the bus. There's no specific reason why it is this particular preposition other than that the verb requires it for that particular phrase. It's a phrasal verb, and its prepositional object is part of that verb phrase.
Let me add another item:
Wir warten auf dem Bahnhofsvorplatz auf den Bus.
This on the other hand isn't a prepositional object but an adverbial. Here, that preposition auf has a certain meaning on its own: with dative case, it tells the location.
And in German you have to tell both apart from separable prefixes, of which many resemble prepositions.
Wir warten mit Geschenken auf.
That auf isn't a preposition at all. It's a separable prefix of the verb aufwarten mit etwas — to come up with something. It's again a phrasal verb that requires a prepositional object mit+Dativ that tells what you donate.
(If you are curious: it's exactly the same in English, isn't it? German and English are truly brethren.)
No, prepositions can also appear in adverbials: Ich fahre im August mit meiner Frau nach Rom.
...plus, they can function as modifiers to a noun, like in the answer to your other question, "die Tiere in den Ställen". (I am new here, don't know how to insert a link to another discussion).
