Hello Dita
I'm also an English learner. May I put my two cents?
WOULD:
[1] I wish you would not do that.
[2] I wish you had not done that.
#1 and #2 are different in the meaning. #1 is: I want you to stop doing that, but I guess it would be impossible for you. #2 is: I regret your doing that in the past.
SUPPOSE:
[1] Suppose someone recognized you.
[2] Suppose someone recognize you.
#1 implies someone's recognizing you is almost unrealistic, whereas #2 implies it is possible.
I'D RATHER:
[1] I'd rather we stayed at home tonight.
[2] I'd rather we stay at home tonight.
There is not much difference in the meaning between #1 and #2. #2 sounds a bit more formal and a bit more polite. So people prefer the construct of #1 when they use it in requesting something to other person politely. (EX) I'd rather you stayed at home tonight.
paco