Zero divided by anything is always zero.
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Yes.
No. Not if the second number is zero.
When the quotient of two integers is positive, either both integers are positive or both negative. When the quotient of two integers is negative, one of the integers is positive and one negative. When the quotient of two integers is zero, the first integer is zero and the second one is anything but zero.
As long as the number is not zero, the quotient remains unchanged. If the multiplier is zero then the quotient is undefined.