Particles: は vs. が vs. を

Okay I was going to ask my sensei about this today but he has influenza, and this is really bugging me. :p

Here is how I understand it.

は is not used to mark a subject.** は is used to draw attention to the fact that the word that precedes it with the predicate in the sentence. It has a sense of "at least". So if you said "これはてがみです。" It's like saying "This, at least, is a letter." It has a sense of like There may be other objects in the world that are letters, but I'm not really concerned about those right now.

**I've also seen は used with objects, like ケーキはたべます。 In this sense I understand it to be like I'm eating cake, but what I am eating is not limited to cake.

Oh, and I gather that は can't be used with unfamiliar topics. Which is why you can't say だれはきますか。

が seems to be used to draw attention and emphasis to the subject of the sentence rather than the actual occurrence. So 山本さんがきませんよ。 would be like saying, Yamamoto isn't coming.　It would be like saying that Yamamoto is the one who isn't coming, focusing more on Yamamoto.

が is used with question words to show emphasis since you can't use は.

を must be similar to が, but used for objects rather than "subjects". (I'm hesitant to say subjects.) It is for emphasis on the object. Back to the earlier example ケーキはたべます。 I'm saying that I'm eating cake, but I'm not commenting on the fact that I may eat other things as well. ケーキをたべます。 -- I am eating the cake [specifically].

Yey for Japanese grammar. Okay, fix my errors.

は vs が

は is traditionally called the "topic marker", meaning it marks the topic of the sentence. Easy enough. It can also be used in contrast but that's a tad more complex grammar. It also indicates that the topic is known to both parties, that is why in sentences such as 「猫がこの部屋にあるか？」 you use が because the speaker does not know if there is a cat in the room. You do not use は.

が is traditionally called the "subject marker" though some people find that an inapt name. Grammatically speaking, yes が does mark the subject of the sentence, but it also marks an unknown. Thus question words are always followed by が, not は.

And yes, が does show more emphasis than は. So sometimes it is used instead.

を vs が

This is rather easy.

を is used to mark the direct object of a transitive verb.

が is used to mark the indirect object of an intransitive verb, thus why it is used with the potential form.

The particles have other uses too but I assumed that this was the context we're talking about.

Oh, and particles have pecking orders, so when the object and the topic are the same, は is used. Only で　and に can coexist with は, such as では and には.