First of all, I like your avatar, it looks rather cute!
Back to your question about "Cha Qi" (I believe you can find the rest of all other terms, huigan etc in much more satisfactory answers, if not, please ask again and will find you some more info), sometime ago (one or two years ago) I posted almost the same question on this forum under puerh tea section and there were some interesting discussions, and me being lazy, I'm not border to dig it out as I found a much better online article which can give you some enlightenment about the mystical term "Cha Qi", it's in Chinese though and don't expect Google Translate would do a wonderful job on it as the article was written in rather advance level of Chinese and it uses a lot of interesting to read but hard to translate idioms ... you need to read between the lines to make some sense.http://dadianhao.com/viewthread.php?tid=870&extra=
The person / people (Da Dian) who wrote this article is / are tea vendor in China, some might say he / they might have an agenda (to sell you more of their tea) behind it. Nevertheless, I think the article have some good arguments and valid points which I don't always find else where.
Anyhow, without infringing the author copyright, as well as it's rather late now here in the UK, I will give some summary of the article.
There are several different meanings / definition when someone use term "Cha.
1. This term is related to the ethos of Taoism and this makes it rather difficult to describe the exact meaning of it. The "Qi" in Cha Qi is related to the Qi as in "Qi Gong" which channelling of inner energy ... etc. Not everyone can understand or feel it. There is no satisfactory scientific explanation. (apache: Taoism's Qi is way beyond my depth and I have to leave it likes this!)
There is a putative scientific explanation and it's related to "Organic Germanium". Some might say OG is deep underground and only ancient trees with their very deep roots can have access to it from the soil, but this is not verified in science.
2. It means whether the tea is strong or weak, is it bitter or mild. But this definition does not give endorsement of the tea quality, whereas the previous definition does.
It's a fashionable term, everyone talks about it when drinking tea. It is like "Emperor New Clothes", one feel embarrass to admit one didn't feel it, if you are served with some very expensive antique aged puerh ...
3. After steeping some tea leaves 30 times and you still can sense the remaining taste, this is "Qi" which everyone can feel and understand this kind of Qi.