The treatments you mentioned are just topical (they treat the skin). The best way to clear the virus is to keep your immune system strong. There are lots of ways you can do this; eat lots of green leafy vegetables, get enough sleep, stay away from refined sugar, manage your stress and if you smoke - stop. Also, there are vitamins and supplements that help your immune system too. I've been looking into Papillex, a supplement that was formulated specifically for HPV, but basically supports your immune system. All of this stuff just supports your body so it can take care of itself - it should help with both high and low risk strains. Hope this helps!
Yes, but they are not cured by medicine, only treated. They go away when your body finally puts the virus in check. Only your own immune system can cure you of HPV. Luckily, low risk HPV (wart causing) strains typically clear more rapidly than high risk ones.