We are in Germany and Austria for 3 weeks. First week is on a river cruise and our tour co. says visa's are not required while on this trip. Do we need visa's when we are on our own?
No, assuming you are U.S. citizens. If so, you can stay for 90 days in the Schengen zone without applying for an extended visa.
As stated, nope. You will receive a stamp when you arrive in the EU. You can stay for 90 days from this point in any of the schengen countries. http://en.wikipedia.org/wiki/Schengen_Area