Dear sir, 1) What is the difference about " believe" and "trust"? If you «believe» something, you think it is true. If you «trust» someone, you think what he says is true.
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Goldmund
3) They often go to bar/night-club in the weekend/in weekend.
Use «to a bar» or «to a night club». Use «at the weekend».
In AmE, we'd say 'on the weekend', or possibly, 'at the week's end'.