Learn German: Du arbeitest sehr gut, danke. - You work very well, thank you.

When you use du (informal 'you'), verbs usually end in -st. But because the base of arbeiten (to work) ends in a 't' (arbeit-), German adds an extra 'e' to make it easier to pronounce. So it becomes arbeitest instead of arbeitst.

Could I use Sie instead of du here?

Yes! If you were speaking to someone formally, like a polite stranger or a client, you would use Sie instead of du. The sentence would then be Sie arbeiten sehr gut, danke. You use du for friends, family, and children.

Doesn't gut mean 'good'? Why is it translated as 'well' here?

In English, we have different words: 'good' describes a thing, and 'well' describes how an action is done. German makes this easier by using the exact same word for both! So gut translates to 'well' when talking about how someone works.

Is danke a verb in this sentence?

Not in this sentence. While it is related to the verb danken (to thank), here it is just used as a fixed everyday expression meaning 'thank you'. It is just added to the end of the sentence to be polite, exactly like in English.