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I started finally learning kanji's readings not only meanings and words. And in two sources I use I see that 何's kun'yomi is なん、なに and on' is カ.
I've seen 何 in many words as
なん: 何度、何と、何で
なに: 何人、何か
ど: 何処、何の
何れ (いずれ)、何時(いつ)
But never as カ. Are there any words that is it as カ?
You are correct that there are many more common uses of the 訓読み なに or なん for 何 when compared with the words which use the 音読み カ.
But here is one example: The word for 'geometry' is:
幾何学 (きかがく) - definition
Although it also seems to appear in words like 如何せん (いかんせん) or 如何 (いかが), I don't think those are strictly standard usages of the readings but more of a jukujikun type (reading by meaning). For example, い is not a standard reading of the kanji 如 (see here for details). Therefore I'm not sure that 如何 qualifies as a usage of the 音読み here.
There are probably more examples - I will check and edit in others if I find them.
According to kanshudo.com counts, 幾何 and its derivatives are the only words that can be encountered among the frequent lexicon. However, there is at least [誰何]{すいか}する “challenging (an unknown person); asking a person's identity” which is rare but still completely recognizable.
Of course, any (Classical) Chinese word can theoretically be a Japanese one read like this; from the 四字熟語 list at http://www.edrdg.org/projects/yojijukugo.html I find [無何之郷]{むかのきょう} [無何有郷]{むかゆうきょう}.
