"The woman starts to fight."
Translation:A nő harcolni kezd.
I feel with both examples, it would be better to use a verb with el- prefixed. (Of course learners wouldn't know it at this point but I think it's good to be aware.) Also, kezdődött.
This may be a matter of preference but for me, a sole "éppen" doesn't sound too good for "just". "Éppenhogy elkezdődött", "Épp most kezdődött (el)", "Épp csak elkezdődött" all sound much better for me.