I am your father

Let the statements be denoted as followed:

p = Darth Vader is Padme's husband.

q = Padme has a son with Darth Vader.

r = Darth Vader is Luke's father.

Hence, we can rewrite statment 1 as: $(p\to q$ ) ˄ $(q\to r$ )

Then, the statement 2 can be rewritten as: $( -r\to -q$ ) ˄ $( -q\to -p$ )

Since $(q\to r$ ) = $( -r\to -q$ ) and $(p\to q$ ) = $( -q\to -p$ ), both statements are equivalent. Thus, if statement 1 is true, statement 2 is true as well.

If they are husband and wife, then they must have one son called Luke;

Since Luke is not a son of the man, husband and wife cannot be valid.

"No" cannot be correct as valid possibility of true is completely denied;

"Maybe" AND "Not enough information" are the same and therefore contradict to each other once they can be true as answer to this question when not the father of Luke means not of at least from the man's contribution to building blocks of DNA of Luke.

"Yes" becomes certain when "Maybe" and "Not enough information" cannot be different implications and then contradict the answer; as it is an only possible answer remained which does not contradict while it is the major possibility meant to usual case.

Answer: $\boxed{Yes}$