Outside/outdoors: 外 (そと/がい/はず) Inside/middle/center: 中 (なか/ちゅう) Indoors: 内 (ない/うち) Pronunciation changes based on whether kanji is by itself (or with other kanji only), combined with hiragana, or it can be an exception. Be prepared to learn 2-3 pronunciations per kanji. Many are shared or similar though which can make it easier.
Unfortunately, not really. Kanji is taken directly from Chinese Han characters, which in turn decended from pictograms. Each character essentially started out as a picture drawn to represent a thing or concept or phrase, rather than a specific phonetic sound the way the roman alphabet does. Consequently, there isn't really a good way of predicting pronunciation for kanji. Having some background in Chinese can sometimes help you come close to at least _one _ of the pronunciations, but given the way kanji tends to have multiple pronunciations, that's not really all that helpful. So there's nothing for it other than rote memorization.
Although katakana was derived from parts of kanji characters, it is part of a phonetic system, meant to represent sounds, and so is best treated as completely different from kanji in terms of both pronunciation and meaning.
The cool thing about a writing system derived from pictograms however, is that it's possible to make predictions on what a word MEANS based on what's in it. For instance, you can generally assume that anything that has 氵as a component has something to do with water/liquid. For instance 涙 (tears) or 海 (sea). And no matter which part of China or Japan you're in, no matter what wildly different-sounding dialect the locals speak, you can be pretty sure of being able to find yourself a bar just by looking out for the word 酒 =D
Actually, only a few kanji are pictograms, most of them are phonetic-ideographic characters, who have a phonetic element and an element indicating their meaning.
Most of the time the element indicating the meaning is also determined to be the radical, under which it can be found in most kanji dictionaries (as with your example of "liquid".
Since most kanji include a phonetic part, you can actually predict their on'yomi to a certain degree. However, since the kanji got their on'yomi from the Chinese pronunciation, which has different sounds than Japanese and the readings were taken at three different time periods from the Chinese pronunciation none of which are equivalent with the current Chinese pronunciation, it's not as consequent as one would hope for. It's much more consistent in Chinese than in Japanese.
As for examples: バイ 培(バイ) - cultivate, foster 倍(バイ) - double, twice, -times 陪(バイ) - follow, accompany 賠(バイ) - indemnify
As you can see, the right phonetical part is identical, while the right part, which is used as the radical as well, indicates the meaning.
As such, knowing the kanji of a Japanese term often really helps in memorizing or guessing the reading of a word and makes learning Japanese much easier compared to if it had no kanji at all, in my humble opinion.