VC dimension of half spaces over the real line

Question

I'm studying VC dimension and I'm having a little difficulty understanding it. I read lots of explanations, but when I come across this simple exercise I did not get a good intuition. The problem is this:

Find the VC dimension for the following case,

$h (x) = \mathbb{1}_{{a < x}}$, with parameter $a, X \in R$.

The resolution is as follows:

VC-dimension = 1.

(a) It can shatter point $0$, by choosing a to be $2$ and $-2$.

(b) It can not shatter any two points ${x1, x2}, x1 < x2$, because the labeling $x1 = 1$ and $x2=0$ can not be realized.

My doubts are:

1) In item (a) what is parameter $a$? I looked for similar exercises, but there was no concrete explanation about this parameter, what is its function? In this item it takes as equals $2$ and $-2$, with $-2 < 0$ ok, but $2 < 0$, I did not understand, from this conclusion, why it is correct.

2) In item (b) I did not understand the inequality, as he came to the conclusion that $x1 < x2$ can not be realized, why is the inequality $x1 > x2$ not valid?