How to differentiate moods, characters, temperaments, etc?

Those terms can be divided into two groups:

First group, temporary, like mood: 心境, 心情. Those two are close to each other. 心情 is more temporary, can be changed in a second. 心境 is more stable and broad, but it can still be changed by big event.

For example, if you say:

I am happy today. This is a kind of 心情.

I am happy the whole month. This is a kind of 心境.

Obviously, if you are happy in a month, you are happy almost everyday in that month, so most of the time 心情 reflects 心境. But it is not always true, you can have an unhappy day in a happy month.

Second group, stable, like character: 脾气, 性格, 性情. Those three are very close to each other, the difference is very subtitle.

Well, I left 心思 (ideas, thoughts), because it's totally different from the above. I also left 气性, 心性, 性气, 心气, because they are rarely used nowadays.

Hmm, perhaps you're trying too hard, think of synonyms. This list resembles something of a thesaurus entry. In certain situations, you can substitute one for the other, while in a different context, you can't substitute the words, and you would know when to use the correct one from experience while conversing in Chinese.

This is the best way I can explain it: think about the following two words in English: sever and cut. We can say, "sever/cut ties", "sever/cut the rope", but while we can say "let's sever up the steak into little bits", it's much more comfortable to say "let's cut up the steak into little bits". It would be tiring to compare the above words in 90 combinations, but you get the idea.