Translation:I don't like mint very much.
That's the "much", it doesn't explain the "very" (or if it does then which is the Japanese word that means "much" in the sentence?). Without the "あまり" it is just "I don't like mint" with it I still don't see anything that correlates to "very" just "I don't like mint much". Not that "I don't like mint much" and "I don't like mint very much" have radically distinct meanings in English.
Yes. There is a scale on which these fall depending on whether the result is negative or positive (ex: "very much vs. not really", etc.). This is a pretty good explanation: http://www.shiro.jp.net/2012/12/yoku-daitai-takusan-sukoshi-amari.html
Just be aware that とても is a unit of degree and don't confuse it with たくさん which is a unit of amount.
とても嬉しいです。 = I am very happy.
たくさんの本があります。 = There are many books.
I believe that あまり here is meant to soften the sentence. E.g. rather than a hard "I dislike mint" it turns it into something akin to "I don't like mint that much" i.e. I don't like mint, but I don't want to offend by interjecting a strong opinion.
Thinking about it in English though, I'm a bit confused:
- I like mint very much (intensified like)
- I very much like mint (same meaning)
- I don't like mint very much (soften dislike)
- I very much don't like mint (? intensified ?)
I'm (a) unsure whether that last sentence is valid in English, but if it is, it (b) sounds like it's intensifying the dislike of mint, rather than softening the sentence. I tried to look up the sentence construction, but beyond the fact that "very much" is acting as an adverb, I couldn't find anything that answered this question.
I would avoid "I very much do not like mint" in English, IMO. It also clearly has to be a negative sentence, because if we used "dislike" instead of "not like":
- I dislike mint very much (intense dislike)
- I very much dislike mint (same meaning)
くない is a conjugation for い-adjectives (which act like verbs and can end a sentence on their own)
高い high/expensive 高くない not high/not expensive
好き is a な-adjective (it does not have an ending い to conjugate). These types of adjectives act like nouns and require a copula (です、だ) in order to show different inflections.
好きです、好きだ like 好きではありません 、好きじゃない do not like