Chances slim but possible. People have warts on hand.
Very, very, very unlikely. HPV (like herpes) is spread only through direct skin to skin genital contact.
I vaguely remember reading that the two STD experts on the forums have never seen this type of infection in their combined sixty plus years of studying medicine (of course, do not quote me on that).
Regardless, HPV just doesn't transmit in the way you describe.