If you have any positive irrational number, then its negative is also irrational.
If it says "negative irrational", then obviously it is irrational.
The negative of a rational number is also rational.
Not necessarily. Irrational numbers can be negative or positive.
No integer is irrational.
No, they can be rational or irrational. The sign of a number has nothing to do with it.
Unless the integer is fractional it is not an irrational number.