Can the NFC antenna of mobile phone such as the Galaxy S4 or iPhone in addition to their NFC functionality, also be used to read signals from (active) RFID tags/transmitters e.g. from 20ft away not 20cms?
No. By default you can't do this, due to different principles of work and hardware chips. As I mentioned earlier my answer on Physics.SE clarify this.
About other possibilities, there were some projects, that provide external abilities, like Touchtag, which was on a market since 2008 to 2012. I think you can use same idea and then redirect data to audio or usb port. Then you will be need an application, to analyse incoming data.