Add new icons to OpenUI5?

As you already mentioned it's not a good idea to extend the UI5 font for future compatibility reasons. If you already have your own font you can easily register it with UI5 and reference it using a similar url-schema. Instead of sap-icon://funny-icon you could say sap-icon://dparnas-icon/funny-icon.

Here is a sample implementation:

jQuery.sap.require("sap.ui.core.IconPool");
jQuery.sap.require("sap.ui.thirdparty.URI");

(function() {
  var aIconNames = [ "funny-icon", "another-icon" ], // the icon names
    sCollectionName = "dparnas-icon", // the collection name used in the url-schema
    sFontFamily = "DarnasIcons", // the icon font family like defined in your css
    aIconContents = [ "E003", "E004" ]; // the unicode characters to find aIconNames under, same order

  // add the icons the your icon pool
  for (var i = 0; i < aIconNames.length && i < aIconContents.length; i++) {
    sap.ui.core.IconPool.addIcon(
      aIconNames[i], 
      sCollectionName, 
      sFontFamily, 
      aIconContents[i]
    );
  }
}());

Furthermore you will have to define the font-family in your CSS. That's it! It's easy but hard to find ;)

I tried adding fontawesome icons into my application hope this helps you in generating and using custom icons

 @font-face {  
  font-family: 'fontAwesome';  
  src:url('./css/font-awesome/fonts/fontawesome-webfont.eot?5qvb9g');  
  src:url('./css/font-awesome/fonts/fontawesome-webfont.eot?5qvb9g#iefix') format('embedded-opentype'),  
  url('./css/font-awesome/fonts/fontawesome-webfont.ttf?5qvb9g') format('truetype'),  
  url('./css/font-awesome/font-awesome/fonts/fontawesome-webfont.woff?5qvb9g') format('woff'), 
  url('./css/font-awesome/fonts/fontawesome-webfont.svg?v=4.5.0#fontawesomeregular') format('svg');       
  font-weight: normal;  
  font-style: normal;  
}  
[class^="icon-"], [class*=" icon-"] {  
  font-family: 'fontAwesome';  
  display: inline-block;
  font: normal normal normal 14px/1 FontAwesome;
  font-size: inherit;
  text-rendering: auto;
  -webkit-font-smoothing: antialiased;
  -moz-osx-font-smoothing: grayscale;
}  
.icon-bell:before {  
  content: "\f0f3";  
}

//initialize the icon in Init()
sap.ui.getCore().attachInit(function () {
  //sap.ui.core.IconPool.addIcon(iconName, collectionName, font-family, unicode char code )//icon definition 
  sap.ui.core.IconPool.addIcon('register', 'customfont', 'fontAwesome', 'f0f3'); //adding new icon
})   

//Using the icon
sap-icon://customfont/bell