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No. Zero is neither positive nor negative. You might think of it as being neutral.
a rational number is any number that can be expressed as p/q where p and q are both integers. Since integers can most definitely be positive-- you might know them as the set of Natural numbers-- then yes, a rational number can be positive.
No. The positive integers are {1, 2, 3, 4, 5, ...}. They start at 1 (which is the least positive integer) and progress forever (to infinity). There is no end to the positive integers, so there is no greatest positive integer. Another way to look at it might be to think of any really large integer (a "counting" or "whole" number) and add one. That will create a "next bigger" large number. You can continue to do this infinitely many times.
The positive effect could be that maybe they really like they're new country and they might get adapted to it but some negative effects would be that some people just can't adapt and maybe they cant speak the new foreign language.
It might be clearer if you think of it this way: Multiplication is repeated addition. 2 x 3 is the same as 3 + 3. They both equal 6. 2 x -3 is the same as -3 + -3. They both equal -6. In the first case, you are increasing the amount of positive things. The answer will be positive. In the second case, you are increasing the amount of negative things. The answer will be negative.