Will itch.io take the payment and process taxes after I complete the required information or will it be impossible for someone to pay for one of my products?
I’m not sure about this. I believe it’s possible but haven’t tried it myself. One thing to keep in mind taken from Itch.io “Accepting Payments and Getting Paid” section:
itch.io is not a bank, you should request your earnings from itch.io in a timely manner. If you don’t withdraw earnings from your account older than a year, we may charge a maintenance fee proportional to any unclaimed money older than a year left in your account. (Read more in our Terms of Service)