Regular Expressions with at least 2 0's and at most 1

Question

I think the answer should be:

$(1+ \epsilon)000^* + 0^*0(1+\epsilon)00^* + 000^*(1+\epsilon)$

But I am not sure if this is the right answer. Can someone explain the correct answer? And if it is correct how can I shorten this up?

Also what is the nfa for the regular expression: ∅*

i have one more problem: i can't surely understand the meaning of Σ* symbol. As far as I understand it should be (0+1)* if Σ = (0, 1) and (a+b+c)* if Σ = (a,b,c) and so on. Please someone clarify this.