You mentioned that selfupdate fails, because permission is denied. This means you didn't use sudo, which you must do:
sudo port selfupdate
You also mentioned that ipe crashes because it links with libQtGui.4, which links with libpng14.14, which doesn't exist. The fact that you have anything still linking with libpng14.14 (instead of libpng16.16), and the fact that your libQtGui.4 is located directly in /opt/local/lib (instead of in /opt/local/libexec/qt4/lib) both indicate that your MacPorts installation is over a year out of date, probably several years. Running sudo port selfupdate and sudo port upgrade outdated should address these issues, although after that much time, it's possible you will run into some upgrade problems. If so, please ask for help on the macports-users mailing list, unless you're sure the problem you're seeing is a bug, in which case please file a ticket here in Trac.
Remember to selfupdate regularly.
