棒和好，它们之间的区别是什么？

Can I use 棒 and 好 interchangeably, when expressing that something is good?
For example：
这是非常棒 / 这是非常好 --> This is very good
我很棒 / 我很好 --> I am (very) good
你的中文很棒 / 你的中文很好 --> Your Chinese is very good

Or is there a difference between them?

The difference is that 棒 is slang/colloquial and would not be used in formal writing.  It is akin to "wanna", "gonna" etc and would be greatly frowned upon.  It shows your educational level when writing say for a resume etc.  Depending on the formal circumstances, 良好, 佳作 (good piece of work) , 流利 (fluency) would be used instead.  It depends on what you want to learn; to speak in daily life or to express oneself in polite society.  Can't speak like a fishmonger's wife in formal circles.

棒和好，它们之间的区别是什么？

Can I use 棒 and 好 interchangeably, when expressing that something is good?
For example：
这是非常棒 / 这是非常好 --> This is very good
我很棒 / 我很好 --> I am (very) good
你的中文很棒 / 你的中文很好 --> Your Chinese is very good
-----------------------
Or is there a difference between them?

“棒”only equals to "好“ when you evaluate something, and its function is only adjective, and it's more used in verbal circumstances.

”好“ has much more meaning and use. for example, when you recovered from a bad health condition, you can say “我(的病)好了。” the “好”here works as a verb, means getting better, or recovered.

The difference between 棒 and 好 is similar to the difference between 'terrific/awesome' and 'good'.

棒和好，它们之间的区别是什么？

Can I use 棒 and 好 interchangeably, when expressing that something is good?
For example：
这是非常棒 / 这是非常好 --> This is very good
我很棒 / 我很好 --> I am (very) good
你的中文很棒 / 你的中文很好 --> Your Chinese is very good

Or is there a difference between them? 

基本没有区别，口语化。