Question 1
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Notice that you are supposed ot assume that that initially you have _ q_0 w as your configuration. This is just to help you detect the "left end" of the tape more easily. So instead of realizing that you are at the end of the tape by the fact that you cannot move left, you cn simply reach the first blang you hit on your way left to realize that.

Question 2
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L' is defined formally, and you should make sure that you understand the definition. I would really hate to see that you miss points on this question because of misunderstanding in the definition level. So, 
L' contains word w exactly when all prefixes of w are in L. For example, 0012 is in L' exactly when
emptystring, 0, 00, 001, 0012 is in L.
Now, if L = {12,123,1,emptystring,12111,233} then L' = { emptystring, 1,12,123}