Yes to both questions.
Penal code 837 provides for citizens to
"arrest another". Technically, in your case, it is the "woman" who is making the arrest; the officer is simply "taking you into custody". Although the Penal Code provide for citizens to arrest another it is rarely done because of possible legal consequences.
Again, yes the "woman" will have to be present and testify at your trial because she is the one who witnessed the alleged offense.
What was the code section you were cited for violating?