a) This is okay. This would be used for example in the following: I was new in the city, just arriving there from the country. And moreover, I was young and inexperienced.
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Henry74I knew that the sky is blueIt sounds completely wrong to my ear. If you are talking about a general fact, it's hard to see how you "knew" it! Did you suddenly forget when you started to say the sentence? If it's a general fact, and you believe that it's a general fact, then it seems to me that you "know" it, not "knew" it.
Henry74I knew that the sky [be] blue, I just didn't remember how beautiful it [be].I would put "was" in both places where you have [be].