Several questions

Hi, I'm Oyo. I live in the US now, but I'm moving to Germany in less than a month (staying for a year as an exchange student)

I am becoming obsessed with languages. I hope to learn many before I die. I speak German quite well, and I'm learning Swedish.

I've been watching much anime lately and "magically" have understood where I was entirely dependent on subtitles before. My curiosity is getting the best of me, like Japanese, as you all know, is so different and strange compared to western languages.

I only know basic stuff that I've learned from watching anime, and I know a minimal amount of kanji, hiragana, and katakana.

Here are my random questions which have been bothering me:

-When is "Itoshii wa" or "ora wa" used instead of "watashi wa"? These are gender-specific pronouns of "I".

-How do personal pronouns sometimes, seemingly, disappear from sentences? (maybe it's just different forms of them that I'm not recognising)

-Why does, for instance, "Keitaro wa" mean "Where's Keitaro"? Wouldn't a "ka" particle make more sense?

-Is "mas" a particle-like "wa" or "ka", or is it just a suffix on various words?

-What does a "mo" particle do? Is it related to verbs or something?

-How do verbs conjugate, if at all, and where do they go in the word order?

-When are kanji used in written Japanese? Could you write in all hiragana, or would that be stupid? (I know it wouldn't be "proper", but would it be understood?)

I guess that's all I can think of at the moment.

By the way, I love these smilies.

you could write it in hiragana, but since japanese has an excessive amount of words that sound the same but mean different things, writing it all phonetically would make it extemely confusing to read.

"Keitaro wa" is just one of those things. The rest of the question is understood and taken in context. It is very informal.
Masu is not a particle, it is an ending in the present tense and on the same level as desu in polite speaking.
"mo" typically means, and, in addition, with that type of thing. like "kore mo" However the meaning can be modified by other words in the phrase. Also, other particles may be more correct in some instances when you want to say "and" or "with" specificially "to"
"ore" and such ways of saying "I" are gender and situation/politeness specific. "I" can also be said by watakushi, boku, and a few others.

For the "Keitaro wa?" thing, it might make more sense to you to think of it as "What about Keitaro?" (which is still odd-sounding but at least it's in the form of a question

To clarify Mandylion's response, ore is used in casual conversation with friends and family. Watashi is a more modest term, used with superiors and strangers I think. It's more respectful than ore.

Personal pronouns DO disappear from sentences In Japanese it's perfectly ok to have a sentence without any subject. It's taken from the context of the rest of the discussion (like everything else in the language! . If you're talking about Keitaro, you don't really need to say 'Keitaro' or 'he' in every single sentence, it's implied. To use your example... "Where's Keitaro?" - "Is over there." (Would that be "asoko da"? "asoko ni iru"?) It's implied that *Keitaro* is over there.