First, there is no such word as "fastly", so you definitely have to use "fast", even if "fastly" seems right in a given context. As for the rest of them, it all depends on whether you need an adjective (no -ly) to describe a noun or an adverb of manner (with -ly) to describe a verb. If you get the principle from just 2 and 3, you've got the idea for the whole set.
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