These mean the same, although both of them have a range of meanings. "She walks the most gracefully." She is compared to other people. "She walks most gracefully." Means she walks very gracefully. Is it wrong to say that we can use or omit "the" before "best" with an adverb without any change of meaning, but when we use "most" with an adverb, the meaning of the sentence changes?
"She walks most gracefully." v "She walks the most gracefully." However, "You're the best!" as a complete sentence can also be an expression of gratitude, meaning "You're awesome!" - whereas "You're best" rarely if ever has this meaning. If the statement was made in the context of a particular discussion (for example, about tennis), the two would have the same meaning (and the same range of meanings that we saw in the previous examples).
I hope we can both agree this sentence is wrong because "good" is an adjective, and cannot be the subject of "is". These clauses are not questions, so the last one should also not be a question. On the linked page, best is used as an adverb,modifying the verb knew.In that context, the phrase the best can also be used as if it were an adverb.The meaning is approximately the same in that case.
So, the version without the "the" carries both meanings (or sets of meanings). But "she walks most gracefully" could also be used to mean "she walks the most gracefully". "She walks most gracefully" could be a synonym for "She walks very gracefully". Alternatively, it could mean that she walks more gracefully than she performs other activities - this is unusual, but would be clear from the context.
Either is acceptable, and the practical meaning is the same, but their referents, implicit not explicit, order are different. See similar questions with these tags. Find the answer to your question by asking.
The adjective best is used in a copular construction with the dummy pronoun it. Here, we have the adjective best, but this adjective is attached to no noun. Because the noun car is modified by the superlative adjective best, and because this makes the noun car definite in this context, we use the.