1.good is only an adjective, not an adverb, and the adverb form is well. For example:
He speaks English very well. He speaks English very well.
He speaks English very well. He speaks English very well.
2.well can be used as both adverb and adjective. When used as an adjective, its usage is very limited and it only means "healthy", "appropriate" or "satisfactory". For example:
She's fine. She is in good health.
Everything is going well with us. Everything is going well with us.
Note: Generally speaking, when well is used as an adjective, it is only used as an predicative rather than an attribute (as in the above example), but in American English, when well means "good health", it can sometimes be used as an attribute.
Second, compare the usage of related phrases.
Good at and good at: both can mean "good at". For example:
He is good at languages. He is good at learning languages.
She is good at telling stories. She is good at telling stories.
They all did well in the exam. They all did well in this exam.
Note: When you are good at a subject, you can also use be good in. For example:
He is good at math. He is good at math.
As good as and as well: used in the original meaning, both can mean "as good", but good is an adjective and well is an adverb. For example:
He speaks English as well as she does.
He speaks English as well as she does.
His English is as good as hers.
But when used in the extended meaning, the two meanings are quite different: as good as means "almost" and "almost" (= almost), as and "and". For example:
The work is almost finished. The work is almost finished.
He is tantamount to calling me a liar. He is tantamount to calling me a liar.
She is both beautiful and clever. She is not only beautiful, but also clever.
Not only did he break his leg, but he also hurt his arm. Not only did he break his leg, but he also hurt his arm.
I hope it helps you, and I wish you progress.