Welcome to the forum. Thank you for researching the topic before asking your questions. And they are excellent questions indeed -- in fact, I'm going to use this as an opportunity for a blog-like response, so that future questioners can be referred to it when appropriate.
It is not uncommon for warts to first appear as long as 2 years after being infected with HPV. It can be as quick as 2-3 months but averages 6-9 months, and can take well over 2 years. At this point, it really isn't possible to know whether she acquired her infection from you or a former partner; because of such long incubation periods, it often isn't possible to figure out when and from whom HPV was acquired. And at this point it doesn't matter. You can assume you have (or have had) the same HPV infection; if you weren't the source, you have been repeatedly exposed and undoubtedly infected. You should keep your eyes out for penile warts -- but as you know many infections remain asymptomatic and you may never develop visible warts.
To your specific questions:
1) Visual diagnosis of warts is highly reliable. Although the doc has some misunderstanding about HPV, if s/he is a typical gynecologist or primary care physician, probably s/he has managed many, many cases and the diganosis can be trusted.
2) I agree your partner's doctor has some misconceptions -- but they are very common ones and you shouldn't fault him or her too strongly. Much knowledge about HPV and warts has been changing over the years and it can be difficult to keep up; and some issues remain open to debate among the experts. S/he is correct that pregnancy often results in recurrent warts, but stress probably has no effect. Whether HPV infected people invariably "carry the virus forever" is a matter of scientific debate. In the large majority of cases, the infection clears up to a point that it cannot be detected, even with the most sophisticated tests, cannot be transmitted, and never reappears in visible form. So for practical purposes, in most infected persons the immune system eventually cures the infection.
3) Yes, this sounds like a typical case of genital and anal warts. It's very common to have warts in multiple locations, including the anal area. Developing anal warts does not depend on direct sexual exposure. Contact with your scrotum is a less likely explanation than the simple fact that the virus can spread to nearby areas, either directly or by scratching, wiping after toilet, etc.
4) There are many choices for treatment. None are perfect; all options work well in 60-70% of patients, and imiquimod (Aldara) is no better (and no worse) than others. Other choices are podofilox (Condylox is the main brand) and sinecatechins (Veregen), which like imiquimod allow treatment at home by the patient; and options that require office treatment, including podophyllin, bi- or trichloroacetic acid, freezing with liquid nitrogen, and wart removal/destruction by laser, electrocautery, or surgery. The latter types are typically used by dermatologists. If you partner's warts don't respond quickly to imiquimod, she should consider seeing a dermatologist for additoinal options.
Vaccination would have no effect on your partner's warts, nor would it protect you, since we can safely assume you are already infected. However, it would protect against future infections in the event either of you is likely to have other sexual partnerships.
I hope this has helped. The bottom line is that all this should be looked at as an inconvenience, not a serious health threat. In the long run, this will fade into a non-event in your partner's health and your relationship together.
Regards-- HHH, MD
Additional brief comment: I meant to also say that there is no need for you and your partner to start using condoms or otherwise altering your sexual practices with one another. That horse is long out of the barn; you're already infected and people don't "ping pong" HPV infections back and forth. However, Aldara treatment is likely to be irritating and for comfort it would be best to avoid sexual contact with the infected tissues if she develops soreness etc at the treatment sites.
Thank you for your advice. I appreciate it very much. I did have one last question that I forgot to ask. I have had a plantar wart in the past and while it was annoying it wasn't a big deal. Do genital warts behave in a similar way as these or other regular warts other than their location?
Yes. All warts have strong similarities in natural course. Whether or not your plantar wart was treated or resolved spontaneously, most likely it never reappeared and you haven't had other warts of the hands or feet. Your partner can expect the same outcome for her anogenital warts.
That is all the questions I have. You have been very helpful. Thank you so much.