First countable space and convergent sequences

Question

Let $(\mathbb{R},T)$ be the co countable topological space where $T=\{A \subseteq \mathbb{R}:A^c \, \text{is countable} \}\cup\{\phi\}$. Take $A=\mathbb{R}/\{1\}$, then

1. $\bar{A}=\mathbb{R}$
2. The space is not first countable.
3. There is no sequence in $A$ that converges to $1$.

My lecture notes only prove the third point while mentioning that the first and second are easy to prove. Is there a way to show why these are true?