How do I interpret this conditional expression?

Questions
1

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2

You can use Reduce to make it more explicit, if longer:

Reduce[1/C2 \[Element] Reals && \[CurlyPhi] > 0 &&
  ! ((C1 | C2) \[Element] Reals && C1 + 2 C2 == 0),
 {\[CurlyPhi], C1, C2}]