They’re not vital, but can be included to avoid ambiguity if requred. Note that someone else’s father is “otou-san”.

It’s いきたい “want to go”. The ～たい suffix conjugates as an い-adjective. The English translation is incorrect in that sentence (should be “If we wanted to go see a movie, I want to go to Cineplex”… or something like that – I’m recounting it from memory, here)

Yep, that works. =)

1. We put “wa” after “watashi” and “ga” after “asagohan”. Particles in Japanese are post-positions – they modify the word that comes before them. Particles in Japanese indicate the function the word plays in the sentence – so long as you keep the same particle with the same word, you can rearrange the sentence as much as you like, and not change the meaning of the sentence (though note if you jumble it up too much, people will lose track of what you’re trying to say).

2. You can have two “wa” particles when “wa” is functioning as a contrastive marker. The grammar dictionary explains that “when more than one wa appears in a sentence, the first wa is usually understood to be the topic marker, the second wa is more contrastive than the first one, the third one is more contrastive than the second, and so on”. It then goes to give the example “watashi wa kyou wa tenisu wa shinai” (I won’t play tennis today), though I have to admit, I’m not quite sure whether it’s saying that I’d prefer to play something else today more than tennis some other day, or the vice versa.

Note that you probably won’t encounter a sentence so wa-heavy in real life. Something slighly more realistic would be “otouto wa asagohan ga kirai jyaarimasen ga, watashi wa kirai desu” (My brother doesn’t dislike breakfast, but I do). By the way, the “ga” before the comma is a different particle to the subject marker “ga”, which you’ll be learning about later. Means “but”.

Two “ga” subject marker particles in a sentence is a little more frequent, as “ga” always marks the subject in subordinate clauses (unless that subject is being contrasted).

3. As I’m pretty sure I’ve mentioned to you before, the A wa B ga C structure is one of the standard basic grammar structures in Japanese, which you’re going to see fairly often. You COULD say B ga A wa C (cf note above about particles) but it’s not very natural, so you’re going to get funny looks. Note that A ga B wa C changes the meaning.

The grammar dictionary says “C usually expresses something about B, and ‘B ga C’ expresses something about A”. It goes on to explain there’s basically three categories into which sentences of this structure fall:

a) A is human, and B ga C expresses something about A’s physical and/or mental state – for example, “watashi wa eigo ga wakarimasu” (I understand English) or “otouto wa asagohan ga kiraijanai desu”.
b) B is part of A, and C says something about B, which in turn says something about A – for example, “Maikeru-san wa se ga takai desu” (Michael is tall) or “watashi wa onaka ga suita” (I’m hungry – literally, my stomach is empty).
c) B is a member of A, and C expresses something about B – for example, “jisho wa webusutaa ga iidesu” (On the topic of dictionaries, Webster’s is good

It then goes on to give a list of verbs and adjectives that almost always take the A wa B ga C structure, like “wakaru” or “hoshii” or “suki” or “hazukashii”. And so forth.

Hope this is actually helping, and not just confusing matters further.

Context. =)

Japanese is a very contextual language, and sentences will tend to drop everything that they can get away with and still make sense. Usually the topic is the first thing to go.

On a side note, the second sentence is not a case of the ga particle being used for emphasis. The topic particle は can only be used for known elements – basically the speaker is assuming the listener knows what they’re talking about. Question words, by definition, are not known elements, meaning they cannot take は – they much always use が.

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. =)

“Whose”, but otherwise spot on. =)

That said, a more natural English phrasing might be “Whose river is this? And whose mountain?”