Discrete Structures question. Don't know how to start really rusty, please explain like I'm five.

1. Prove the following identity on languages A, B: (A ∪ B)* = (AB)*

2. For string x, the reversal of x, denoted $x^R$, is defined as , if x= $varepsilon$; and as $x_n$ $x_2$ $x_1$, if x= $x_1$ $x_2$…$x_n$. For language A, the reversal of A, denoted $A^R$, is defined to be
   $A^R$ = { $x^R$ for all x in A }.
   Determine if the following equation is true for all languages A or not. Present a proof or a counterexample: ($A^R$)* = $(A*)^R$

I still don’t really understand what the star symbol means and how that affects the equations.