Can anyone explain what is the difference between そして and それから, and when to use which?
There is an article about the difference (although in Japanese): 「そして」／「それから」の一考察
As shown in the picture below, in a nutshell, this article says that それから involves a shift in viewpoint, while そして adds information from the same viewpoint.
Let me try to explain this.
When you describe something happens after something, basically you can use both そして and それから. But それから more explicitly focuses on the sequence of events (what comes next to something), and often implies the two things happens more or less independently. It's closer to "after that" in English. On the other hand, そして often implies the second thing happens as a result of the first thing ("and" in English).
Today, I'll do my homework, ______ watch TV.
Here, そして and それから are interchangeable, but それから sounds more like "and after that" while そして sounds more like "and then".
I studied seriously, and passed the examination.
Here そして is the natural choice because he passed the exam because he studied seriously. Such reason-result relationships are denoted only by そして. If you used それから here, it would sound like "in addition", which sounds awkward.
You must study seriously first, and after that, take the exam.
Here それから is the natural choice because the speaker is strongly emphasizing the proper order of what you need to do. (Maybe you can forget the picture above in this case)
When you list multiple things, you can use both それから and そして:
He can speak Japanese, English, ______ Spanish.
Here そして and それから are interchangeable, but それから is much less common in formal, written, or organized sentences.
He can speak Japanese and English. Oh, Spanish, too.
Here それから sounds more natural because the speaker was not "seeing" Spanish at first. In conversations, それから is a good word to add something as an afterthought (see this).
Um, let's see ... / And, well, er ...
Actually それから is a common filler word used when the speaker is trying to say something more. Maybe he's trying to "change his viewpoint".
Used as a conjunction there is no difference.
They both can be translated as "and" or "then".
そして can also be used as an adverb meaning "in that way"