Welcome to our Forum and thanks for your questions.  Congratulations as well on your forthcoming marriage.  The sorts of contacts you describe- non-penetrative rubbing. kissing, breast kissing and having your penis licked without it entering a partner's mouth are no risk exposures with no meaningful risk for any STI, including HSV and HPV.  I see no reason for concern and no reason for testing.

In answer to your specific questions:

1. Based on my kissing experience, is there a chance of oral HPV or HSV2? I was not immunized for HPV when I was with the first one.

No, as noted above, these were no risk events.

2. How are the chances of genital HPV, HSV1&2 (especially HSV2) from that brief lick on my genital?

Same answer as above.  These were no risk events.  If you have HSV-1, as many people do, you would have acquired it in childhood as is most often the case, not from the exposures you have described.

3. I know most HPV infections clear out after a while. Is it after 6 months or more? I’ve read different ranges from 6 to 24 months.

Your exposures were no risk but if you had been infected, the infection would have most likely cleared since then.  The reason there is a range is that while most infections clear after 6 months those that remain continue to clear so that he longer the interval, the more likely there is to have been clearance. 

4. Is HPV vaccine effective for oral HPV as well, or it’s just form genital HPV?

Definitive studies are underway but all indications are that the HPV vaccine should protect against oral as well as genital infections.

5. How long does it take for the vaccine to become effective? I had a kissing relationship one week after the first shot of the vaccine? Is that enough time?

The vaccine becomes more effective with the passage of time,  Vaccine activity is protective after the 2nd dose.  HPV is not passed through kissing but the one week have the first vaccine dose would be early to expect protective effect.

6. The fact that sometimes I feel I have irritations in my throat (due to allergies) or gum breaks changes my chances?

No.

7. Do you recommend IgG test for HPV2? I’m very worried for HPV2 but the thought of false negative scares me. Is it necessary or helpful for me? Is it true no matter how long passes there is a chance of error in IgG?

You may mean HSV-2, not HPV.  Either way, in your situation I recommend against blood tests.  They are much more likely to be falsely positive than to find an infection.

8. You think I need to talk about any of these with my future wife? Are there chances of serious health issues or I’ll just cloud her mind with useless thoughts?

I see no reason to discuss these low risk events with your future wife.  The exposures did not put you at risk for infection and if the disclosure would introduce tension into your relationship it would not be a good thing.  I suggest you just move forward from here without concern about these past experiences.  EWH