Asking for English advice on this forum is like asking me the best way to give up smoking...enlightening but hardly trustworthy!
1 - Quick, fast, and quickly - Quick and fast are interchangeable
when used as adjectives but not necessarily in other circumstances;
"Quick" said John "We'll miss the train!" is correct
"Fast" said John "We'll miss the train!" is not
'Quickly' as dj_stick pointed out is an adverb
2 - Your English is/Your English are...'Is' is used where the subject is singular, so in this case the correct one is 'Your English is' because you are talking to one person about their English. If you were talking about
the English it would be 'are' as, unfortunately, there is more than one English person (

). So to recap English (language) - singular - therefore 'is'; English (people) - plural - therefore 'are'.
3 - Good/Well/Nice - Good and Nice are both adjectives (used to describe a noun) so they are interchangeable as in 'Good car' or 'Nice car'. On a side note many people dislike the word 'nice' as it has lost any real meaning. My English teacher went nuts if anyone used the word 'nice'.
Well - This is a bit more tricky, well can be an adverb or an adjective (can also be an interjection or a noun - but you're not asking about that), however, in general usage it is only used as an adjective when talking about someone's health i.e. 'He is well' means he is not sick...
English is (singular!) a bitch of a language because we have so many words that are the same but have different meanings depending on how they are used.