I received my first vaccine shot when I was 16. I'm 23 and now and am currently living with HPV and genital warts. I got my 2nd HPV vaccine dose about a month ago.

Welcome to the Forum and thanks for your questions.  While there are no studies to inform the answers to your questions, I'll be glad to provide some information.  As you point out the schedule for HPV vaccination involves receipt of a 2nd vaccine dose about a month after the first, followed by a 3rd dose at 6 months or beyond.  Single doses of HPV vaccine are not fully protective but after two doses taken using the recommended schedule, most people are protected.  In your situation, out of an abundance of caution, my advice would be to pursue your vaccination as though you'd never been vaccinated before, following your recent vaccination with another injection soon with the final dose to follow in about 6 months.   There is no reason to think that you would be at any risk for adverse events or side effects because of your earlier dose of vaccine 7 years ago.---

Is there any benefit to getting the 2nd dose 2 months after the initial dose vs getting it one month after the initial dose?

I doubt it would make a meaningful difference.  EWH ---

Is inosine pranobex effective treatment for clearing HPV? 

A number of studies indicate that inosine pranobex is effective in stimulating the immune system to treat HPV infections.  Therapies for HPV most typically work in one of two ways- either they actively destroy virus within infected tissue (laser, acids, surgical removal) or they stimulate the immune system to attack the virus and virus infected tissues.  Inosine pranobex is in the latter category.---