Is using the tap and soap of a public bathroom really reducing the chances of virus/bacteria infection? Or is it increasing them because the soap and tap carry viruses and bacteria themselfes?
Not unless you go out of your way to avoid touching everything. The act of washing with soap and water removes your personal fecal bacteria and turning off the water replaces it with whatever filth is on the knobs. Ditto if you touch the door knob/handle on the way out.
Not sure if you've been to Japan but they have some of the cleanest public facilities I've seen in spite of all the traffic. I'm sure people are coming through multiple times a day to wipe down all fomites.
Fomite - Wikipedia: A fomes or fomite is any inanimate object that, when contaminated with or exposed to infectious agents can transfer disease to a new host. E.g. tap, couch, bench, hat.
Touching the soap doesn’t matter at all. You’re about to wash it all off your hands.
Soap and water definitely work to reduce infections, even when using a shared sink. Look up what happened in the 19th century when people finally figured this out and started hand washing regularly, infectious disease transmission in settings like hospitals dropped dramatically.
I believe I did answer your question. Washing your hands will always be better than not. Many modern buildings also have automated water/soap/towel dispensers. And you can always use the towel to open the door.
Yes, but on your way into the stall, you touched the stall door, and then you touched other things, including your clothing, which you didn't wash on the way out, only your hands.
Germs probably survive better on your skin than on the cold metal tap in the bathroom. Food safe handwashing says use a paper towel to turn off the tap after you are done drying your hands with it.