AI means "love" and SHITEIRU means "doing", so AISHITEIRU can be directly translated as "LOVING" (verb, not adjective!).
Ahhh. "Yesterday" is KINOU. In the Japanese language, you have to remember which words have long "o"s and which ones don't, because they have different meanings. Also remember that "ou" and "oo" can be spelt as "oh", but "oo" and "ou" are not interchangeable.
KORE literally means "this". :)
Okay, it's difficult to explain the WO, GA, WA, etc because I never took formal classes, and I learned how to use them solely from experience.
WA and GA both mean "is", although you must note that because often Japanese cannot be directly translated into English, there may not necessarily be an "is" in the English equivalent of the phrase.
WO comes right before an action, or a verb. It shows that you are doing something to the object/action/person in the word that comes before the WO; for example, doa wo akeru ---> "open the door".
KA is used to turn any statement into a question, although as you gain experience you will come across situations where KA can be used in slightly different contexts. Again, it's difficult to explain because all this comes with experience, and you'd have to speak the language as much as possible to understand. You're right, there aren't really equivalent words for these articles in English. :)
DESU doesn't have a meaning - many people say it means "is/are", but I think that's wrong. DESU is just an end to a sentence - but when you say DESU GA, you're "ending" a sentence and then going "but...".
Yup, KAZE is "wind". :D