The expressions/phrases that involve 気 (ie: 気になる, 気にする, 気がついた, etc) are pretty well documented online. However, it seems difficult to find how to use 気 outside of these. For example, I recently encountered:
逃げる気ですね、優希ちゃん
(saying that Yuuki seems to be running away with the game)
何になる気だ
(asking "what will you become?" after another character says they will lose their human form)
In the first example, 気 to be functioning a bit like みたい or よう, while in the second, I'm not exactly sure what it is doing.
While I'd like an answer addressing what is being expressed in these examples, I would also like a more general coverage of how 気 is used outside of expressions.