AはBがC is a fairly standard structure when describing something. Basically, C describes something about B, and BがC describes something about A. A is the topic, while B is the subject. Basically, “On the topic of A, (his/her/its) B is C”. The grammar dictionary’s got a more complete (but complex) explanation, if you’d like me to dig it out. =)

Keep in mind, you’re probably getting a little bit confused by the fact that “like” is a verb in English, but an adjective in Japanese. In English, “rain” would be the direct object in “My father likes rain”, but Japanese, あめ is the subject instead.

Your translations are correct, though depending on context, the second could be “adults” (rather than “an adult”), while the third could be “What do you like?” or “What would you like?”. Or even “What would he/she like?”. Japanese is a much more contextual language than English. =)

Um. Mostly, I think. It kinda seems a little bit odd to do it with いくら, but with other question words it’s fine, though the usage is a bit different. You could say, for example, こういち　は　だれ　ですか (Who is Kouichi), which’d mean “please tell me about Kouichi”. Or you could say だれ　が　こういち　ですか, which’d mean “which person in that group of people standing over there is Kouchi?”. Like I said, though, it doesn’t really work so much with いくら.

“Whatever’s in front of が is the subject” is basically another way of saying “が marks the subject” or “が is the subject marker”. Basically, all particles in Japanese are post-positions – they modify the word that comes before them. Particles define the function a word plays in a sentence – so long as you keep the same particles with the same words, you can rearrange the sentence all you like and still retain the same meaning (though if things start getting too jumbled, it starts getting a little difficult for a listener keep track of what’s going on).