Is it possible to contract genital warts or herpes as the result of a handjob? I will qualify this in that my situation involves a handjob from a masseuse with no cuts
Theoretically possible, but the chance of it happening is so low, it is practically imposible. Many doctors say that HPV is not spread this way at all, and I agree with them.
I would tend to agree. I've read a couple of studies, finding that it can and has happened, but I was not able to glean from the studies the context in which it happened. For example, did the person passing HPV touch their genitals and then touch their partner's genitalia?
Is it possible to transfer HPV via a shared bed sheet?
I would not worry about transfer via a bedsheet. I have never heard of this happening. Almost every case of transmission is via direct genital to genital, or genital to oral contact.