In the first sentence, "as" can be replaced with "because." So, "because" or "as" in this sentence indicates a transition in the sentence from "what" the speaker wants to "why" the speaker wants that particular outcome. He/she hopes that the people will come so that he/she can hear about the trip. In the second sentence, "because" indicates a causal transition from the first part to the second. Again, as in the first sentence, a reason is being provided as to why the dessert is all gone: "because" someone ate it all the night before. In the third sentence, "since" offers yet another transition indicating yet another reason. The items (whatever they are) are expensive because they are difficult to obtain. In sentences one and three, the words in question are adverbs, in sentence two, "because" is a conjunction.