They're good questions, and I have a positive answer--you can't spread warts by touching. Think about all the people who have warts one place or another (if you can't think of any, come to my office and I'll introduce you to some.) The warts are on the hands, or on the face, or on the feet. Everybody washes themselves, and if the warts could spread by touching, wouldn't we all be covered in warts? But we're not! And you won't be either.
By the way, why not get rid of your warts? The ones you have sound easy enough.
Best.
Dr. Rockoff