Q1) How is this symbol read as $±$? 

"Plus AND Minus" or Plus OR Minus"?

All this time I've been reading it as Plus-Minus.

I asked my math teacher and he said it's the former one. Then my question is if it's "Plus AND Minus" then when we take square roots on both sides of an equation, like,

$$x^2 = 9 \implies x= ± 3 $$

How can we say $x$ equals $2$ values? It should be $+3$ or $-3$ right?

Q2) My teacher said, $$|x| ≠ ± x$$ but $$|x| = 5 \implies x = ±5$$

Wait... what? What is going on here? I think I lack the basic math knowledge here. 

EDIT: I forgot to mention another thing.

He says, $$\sqrt{9} = 3$$

And then he says, $$\sqrt{x^2}= |x|$$ but wouldn't that mean of $$\sqrt{9} = |3|$$ & $$ |3| = ± 3$$ Didn't he just contradict himself?

Thanks :)