Unlike English letters (and, for that matter, unlike the kana), kanji in Japanese all have inherent meaning. However, for the most part, they need to form words by coming together with other kanji and/or hiragana endings – though some words consist of just a single kanji on its own, 才 doesn’t do that.

Which is to say, to form the word meaning “genius”, you need to take the kanji meaning “genius” and stick the kanji meaning “heaven” on the front of it. 天才.

Yeah, it means “genius”. It’s just not used in sentences like that. =)

Also means “years old” and “cubic shaku” (a shaku is a unit of linear distance which is about a foot long).

An advantage of knowing kanji meanings is that they help you to work out meanings of words you’ve never seen before. For example, suppose you encounter the word 空気 for the first time, but you happen to know that 空 means “sky” and 気 means “air”. You’d probably guess, then, that 空気 means “atmosphere” – and you’d be correct.