1. While I’ve heard something similar, I think it’s meant for men…
3. I highly doubt it. The half-hour is probably the half-hour
that the flame is meant to burn to fulfill the mitzvah.
I assume you’re meant to look at it during that time.
As far as the Tehillim goes, would that be R’ Nachman of Breslov’s
“Tikkun HaKlali?” That’s definitely (primarily) for men.
You should be able to Google it… eh, I’ll just do it myself.
OK, according to Wikipedia(!), “The Tikkun HaKlali consists of the following ten Psalms said in this order:
16, 32, 41, 42, 59, 77, 90, 105, 137, and 150,” and
“Women also recite it as a general rectification for sin.”
Ah freilichen Chanukah (and please ask a doctor if it is advisable to stare at a candle for 30 minutes before doing so)!