1. The correct answer is C. piping hot and spicy.
Absolute phrases are phrases you would use to refer to a particular noun usually, in order to describe it in further detail. They never contain a finite verb, so the answer here is C. That phrase describes the noun food, saying what the food is like. Absolute phrases are not essential within a sentence.
2. The correct answer is A. Since we want to go the fair, we're going to have to save our money.
These two sentences are connected by a particular condition. That condition is that we need money in order to go to the fair. If we don't have money, then we won't be able to go to the fair. The only option that shows this relationship is sentence A.
3. The correct answer is C. because.
First of all, it is the only conjunction among these examples. Option A is a sentence, not a conjunction. Option B is an adjective, not a conjunction. Option D is also not a conjunction, but rather semi-colons and commas. The only conjunction is the word because. Subordinate conjunctions connect a subordinate sentence with an independent one.