1. I called on one of my friends in Quebec.
- This is fine.
2. What's the difference between
yesterday, I ran across Dave in the city.
yesterday, I ran into Dave in the city.
- It would probably be more common to say 'I came across...' rather than 'I ran across...' but people would know what you mean.
3. If I put this poem into Japanese, I will be little strange.
- "If I put this poem in Japanese, it would be a little strange"
or probably more correctly
- "If I translated this poem into Japanese, it would be a little strange"
4. There are some people who counter my opinion.
- I think this is fine, though variations might be "There are some people who have a different opinion" or "There are some people who argue against my opinion".
5. There was a considerable rise of the birthrate in 1990.
- "There was a considerable rise in the birthrate in 1990"
6. He always lags behind his work.
- "He always lags behind in his work"
or
- "He always lags behind with his work"
7. the civil war in south Africa arose from the religion.
- "the civil war in South Africa was caused by religion."
8. As my grandma has to take care of my grandpa all the time, he is a burden for her.
- This is fine. "...he is a burden to her." is also ok.
9. If you just smile when you don't understand what others say, you imply you did understood everything.
- "If you just smile when you don't understand what others say, you imply that you understood everything."
10. Teachers at school always impose their rules on pupils.
- This is fine.