So we don't have any same-sex transmission studies for hsv2, unfortunately. Generally speaking, women who have sex with women have the lowest STD transmission rates of any group. I'll do my best to answer your questions, but keep in mind that some things will be best guesses.
1) What is the risk level for performing oral sex unprotected on her if she does not have an outbreak?
Oral hsv2 is uncommon, and when it does happen, it rarely recurs, rarely sheds, and therefore almost never transmits. Herpes also doesn't go as easily from the genitals to the mouth as it does from the mouth to the genitals.
2) Is it advisable to use a dental dam for oral sex on her, regardless of an outbreak or not?
You can, if it makes you feel better. Most people don't.
3) Would a dental dam protect me fully from risk?
Yes, but the risk is really low.
4) Is there anyway to have safe genital/genital contact with her or should this be avoided?
As I said, we don't have transmission stats for same sex partners. We do for opposite sex partners, though, so let me give you those. As I said, women having sex with other women have the lowest transmission rates of all STDs, so I'm going to use the lowest transmission rates we have, which is female to male.
These rates are assuming a long term, monogamous relationship, sex 2-3x a week, and avoiding sex with any symptoms.
Only avoiding sex during an outbreak - 4-5%
Adding condoms OR daily antivirals - 2-3%
Adding condoms AND daily antivirals - 1-2%
So basically, at best, since she's on antivirals, you have a 2-3% chance of getting it a year. I'd expect it to be lower.
I mentioned earlier that herpes goes from the mouth to the genitals. Normally, your oral hsv1 can be transmitted to someone via oral sex, causing genital herpes type 1. Because she has hsv2, that gives her strong protection against hsv1. Unfortunately, your hsv1 doesn't offer protection against hsv2.
Also, I agree that your equivocal hsv2 test probably is a negative.
Hope this helps. Let me know what other questions you have or if I missed any.