I'm guessing you want someone to correct your English and not the factual accuracy of what you have written. Your writing was generally good, but it was sometimes difficult (for me, at least!) to understand what you wanted to say because of your punctuation, but, based on what I think you were trying to say, here's how I would have written it:
"People usually say 'zaijian' when they leave each other. However, when two friends part, they would say 'huijian' instead of 'zaijian'. Lovers can also say 'zaijian', but here it means that the relationship is over; normally, they would never say 'huijian' when they break up.
-- Are there any mistakes?"