Append Isolated Points to Compact $T_2$-Space

Question

My question concernes a construction in this article [PDF] at page 185:

Let $X$ be a compact $T_2$-space and $Y$ (resp. $Z$) results of adding one (resp two) isolated point(s) to $X$, then $X \cong Z \not \cong Y$.

Futhermore there is said that $X \oplus X \cong X \oplus Z \cong Y \oplus Y$ holds.

My questions:

1. Why $X \cong Z$ ?

2. " $ X \oplus Z \cong Y \oplus Y$ ?

Here the concerning excerpt:

Answer 1

Your statement of the result, beginning "Let $X$ be a compact $T_2$-space ..." would normally be understood as a statement about all compact $T_2$-spaces. The actual result that Scott quotes from Sundaresan is about one very particular $T_2$-space. The reason $X\cong Z$ is that Sundaresan worked hard to get this property; it's far from automatic. On the other hand, $X\oplus Z\cong Y\oplus Y$ because both of these spaces are just $X\oplus X$ plus two isolated points.