Are all random variables have the same distribution?

Question

In this paper, a variation of Chernoff bound has been introduced.

For $N$ independent 0–1 random variables $X_{1},X_{2},...,X_{N}$ define $X=\sum_{i=1}^{N}X_{i}$. Then with high probability we have

$X \in E[X] + O\big(log(n) + \sqrt{E[X]log(n)}\big)$

I have 2 questions.

1. Are all random variables have the same distribution $Bin(1,p)$? Can they have different distributions ($X_{1}\sim Bin(1,p_{1}),X_{2}\sim Bin(1,p_{2}),...,X_{N}\sim Bin(1,p_{N})$)?
2. What is the meaning of $\in$? Does this mean $X\in \big[E[X] - O\big(log(n) + \sqrt{E[X]log(n)}\big),E[X] + O\big(log(n) + \sqrt{E[X]log(n)}\big)\big]$ ?