Ok, see this youtube video, here is this tense matrix
Past - Present - Future Simple Continuous Perfect Perfect Continuous
We also have the same tense structures for Modals
Can - May - Might - Must - Could - Would - Ought to Simple may do Continuous may be doing Perfect may have done Perfect Continuous may have been doing
I would think the differences between "must live in Japan" & "must be living in Japan" are:
Must here refers to a very high possibility. Things that you think is very likely to happen.
Ex: She must live in Japan (we also have "She lives in Japan" which means she lives there more or less permanently)
And when you want to emphasize a continuous process, say "She must be living in Japan" (we also have "She is living in Japan" which means she lives there more or less temporarily)
Ok, "must, might" are easy, but what about "should"?
My question is that: What are the differences between "I should live in Japan" & "I should be living in Japan"?
Does "I should live in Japan" mean "I should live there more or less permanently"
& "I should be living in Japan" mean "I should live there more or less temporarily"?
Note: "must" here refers to possibility not obligation. She must live in Japan (=it is likely that she lives there at this moment), not (She have to live there) as if it is obligation
"should" here refers to advice.