Okay so first, if someone gets genital herpes from oral sex, they have genital herpes type 1. It doesn't turn into type 2. The number indicates the strain, not the location. Hsv2 is almost always genital. Statistically, I'd assume that's where it is.
So for you, you have definitely seen a reduction in your symptoms with Valtrex? What kind of blood test did you have done? What was the time frame? I ask because ghsv1 recurring like yours does is unusual. Have you ever had one of them cultured? Does Valtrex taken every day reduce the frequency?
Did both of you get IgG testing done? Make sure it was IgG testing, not IgM. IgM testing is highly unreliable. Also, see if you can find out her numbers, as well as yours. Especially with hsv2, anything under a 3.5 needs to be confirmed, as there is a good chance it's a false positive if it's below that.
Now, your questions:
Assumptions: No sexual contact during symptoms. YES.
Mostly use condoms for vaginal or anal sex. Yes, though there is room for debate on this, which I'll address below.
1. Can it be determined if her HSV2 is the actual virus she carries or just antibodies? There is no such thing as being just a carrier or having just been exposed. If she has antibodies, she has herpes, and is infectious.
2. Can it be determined if she has oral or genital HSV2?
Without symptoms, technically no, but oral hsv2 is very rare, so unless she had any oral symptoms, it's safe to assume it's a genital infection.
3. If I am receiving unprotected oral sex, a) can my genital HSV1 be transmitted to her, or b) can I receive HSV2 from her?
a) No. Herpes rarely goes from the genitals to the mouth (though the assumption about not having sexual contact during symptoms is important here), and having hsv2 offers protection against getting hsv1. The reverse is NOT true, though - having hsv1 doesn't protect you from hsv2, though it may make hsv2 more mild.
b) Oral hsv2 is rare, but avoid this if she has any symptoms.
4. If yes, is the only "safe" choice to use condoms for receiving oral sex?
See #3 - not applicable.
5. If I am giving her unprotected oral sex, a) can I give her HSV1, or b) get HSV2?
6. If yes, is a dental dam the only "safe" choice for giving her oral sex?
7. Obviously a condom will help reduce transmission during vaginal or anal sex, but by how much?
So we don't have transmission studies for ghsv1 like we do for ghsv2. We do know shedding rates, though.
Shedding rates: (and you can find all this in the herpes handbook - https://westoverheights.com/herpes/the-updated-herpes-handbook/)
HSV 2 genital 15-30% of days evaluated
HSV 1 genital 3-5% of days evaluated
HSV 1 oral 25% of days evaluated
HSV 2 oral 1% of days evaluated
Ghsv2 transmission rates, female to male, over the course of a year, assuming sex 2-3x a week:
We also know that ghsv1 generally results in far fewer outbreaks than ghsv2, and many people never get another outbreak after their first. That, combined with the lower shedding rates, means lower transmission.
So for transmission rates. We don't know the exact transmission rates for ghsv1, but here are the rates for ghsv2, and if your math is better than mine, maybe you can extrapolate some figures.
Ghsv2 transmission, female to male, over the course of a year, assuming vaginal sex 2-3 times a week (we don't have studies on anal sex):
Only avoiding sex during an outbreak - 4-5%
Adding condoms OR daily suppression - 2-3%
Adding condoms AND daily suppression - 1-2%
8. Do we have to worry about kissing, if neither of us has ever had symptoms (cold sores) in the mouth, but her HSV2 seems to have been acquired by an ex who did have cold sores?
Her hsv2 wasn't acquired by an ex who had cold sores. It was acquired by someone who had hsv2 and didn't know it, perhaps that same guy, I don't know. I explained above that oral hsv1 doesn't turn into ghsv2, it would be ghsv1.
It's possible you also have oral hsv1, or maybe not. Your blood test only tells you what type you have, not where. You can worry about oral hsv1, or you can assume that you have it, and she might have it - the IgG blood test misses 30% of hsv1 infections, and not deprive yourself of kissing your partner. Over half the adult population has hsv1 orally.
9. Is mutual masturbation (hand-job and fingering) safe? Must we wash our hands right after, or can we touch our own genitals after touching the other person’s genitals without washing our hands, and still be safe?
10. Should we *both* take anti-virals (like Valacyclovir) to further minimize risk, on daily basis, or only during symptoms? Or just me daily, or only during symptoms?
Mutual masturbation is always safe. You don't need to wash your hands. You are not walking bio-hazards. The only times ways you can spread genital herpes are by direct skin to skin genital to genital contact, like unclothed grinding, rubbing, penetration, etc.
It's up to you all to decide, together, what prevention methods work best for you, and what you are both comfortable with.
Before making any decisions, I'd get copies of your tests, and I'd get one of your lesions cultured. That's where I'd start.