Assistance with Notation in the Paper Entitled: "Search Through Systematic Set Enumeration"
Please, one question per question.

The answer to your first question: No, prime most likely does not indicate complement, absent some specific indication of that.  It is just another variable.  $e$ is one variable; $e'$ is another variable (the author could have used a different letter, like $f$ or $x$ or something, but chose to use $e'$ instead).

The answer to your second question: The ind function is defined in the text immediately preceding the definition.  Read it again?

Yes, it's possible you might lack the necessary mathematical background.  You might try taking an online course (or working through a textbook) on discrete mathematics for computer science.