2. It's a number, but it is not rational since you cannot simplify it to a fraction such as $\frac{a}{b}$. Infinity is not a number, so you cannot use it as one in a rational expression. However, even though this number is not rational, but it is real based on your given information.
3. It is 0, which happens to equal 1* $10^{-z}$ as z tends to infinity