It is correct to use Faster and Fastly ? or I should use just Fast? in a comparative way and as an adjetive respectively.
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Use "faster" as a comparative "a rabbit is faster than a snail", for example. Use "fast" as an adjective, "a fast car".
If you need the superlative it's "fastest"; "a rabbit is faster than a snail, but a car is the fastest of the three".
If you want an adverb, use "quickly"; "the rabbit moved quickly, for example. "Fastly" is incorrect.