Hi Quoc. Your questions:
1/ What does amagine mean? Is that imagine? Sorry about the mistake! Yes, "imagine", not "amagine".
2/ Does I expect mean I should think or I think or both? What is the difference between I should think and I think ? I should think means the same as I would think. It expresses less certainty than I think. But note that it is a present form, so your first example is not correct. In any case in the negative there is really no difference. .
I expect it will rain = I should think it will rain
I don't expect rain = I don't think it will rain, I shouldn't think it will rain
We were expecting it to rain = we expected it might rain
We weren't expecting it to rain = we didn't think it would rain.
Just another point about "expect". Some of the examples don't sound quite right because the meaning of
expect changes with the construction. With the example of rain there's little difference, but if we're taking about a person we get:
I expect he will help you = I think it is quite probable that he will help you
I expect him to help you = I think he ought to help you