If you have any positive irrational number, then its negative is also irrational.
A negative irrational number can be thought of as an irrational number multiplied by -1, or an irrational number with a minus sign in front of it.
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.
Unless the integer is fractional it is not an irrational number.