About "assumptions", "advice" and "obligation"

Well, I’d like to know the relationship of meaning and usages of the words “should”, “must” and “shall” concerning to the assumptions, obligation and advices.

must is stronger than should . Must is used for giving official instructions, or main rules of something.
Form example; The instruments in NYC says drivers must keep their eyes open …

otherwise, you can use both should and must .I realize native speakers use should more than must …

shall is kind of will although it has a slightly difference, you say I am going to go to Boston -similar to- I shall go to Boston.
people tend to not use it anymore.

I hope it is helpful

I suggest you had better wait for the experts and the couches to explain this because I am not pretty sure .

Thanks for your help!