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1. False.  $L(E)$ $\neq (a+b+c)^*$.. For instance, the String $ba$ can not be produced by the Regular expression.

2. True.  $L(EE)$ = $(a + b + c)^*$.. Try it once.. It's a beautiful question.

3. False. $(L(E))^*$ = $(a + b + c)^*$.... Because we can see that $a,b,c \in L(E)$.. Hence, $(L(E))^* = (a+b+c)^*$.. But from Statement $1$, we already know that  $L(E)$ $\neq (a+b+c)^*$.. Hence, $L(E) \neq (L(E))^*$

4. True. We just saw that $(L(E))^* = (a+b+c)^*$ and from statement $2$ we know that $L(EE)$ = $(a + b + c)^*$...
Hence, $L(EE) = (L(E))^*$