What software has the features I need to replace Skype?
At the moment, I am sticking with uninstalling "new Skype" and going back to the old Skype.

But, VBuzzer is also a very good choice. They are based on open standards and can do most of the above, including video conferencing without a download (i.e.; in browser). (No Skype-in type number though). They also have mobile applications for both iOS and Android.

Google Voice + Gchat + Google Plus hangouts is always an option as well