Next, and my main question, is there some way to customize TinyMCE? I want to remove some options, like the "Font" menu...
Have a look inside FGLASDIR/tpl/SetHtml5/TextEdit.xhtml and look for a line data-g-toolbar. My understanding is that controls the buttons that appear in the toolbar and you'll see an entry "fontselect". So if you don't want the Font menu, remove "fontselect" from this string. (clear browser cache if it doesn't appear to work first time)
My guess is that "data-g-toolbar" is referenced within FGLASDIR/tpl/SetHtml5/components.js (search for gToolbar in this file) inside a function createRTE.editor which in turn somehow invokes the tinymce.init function. Other configuration options could be set here but you would have to reference the tinymce documentation for suitable values. e.g.
http://www.tinymce.com/wiki.php/ConfigurationIf you do make any customisation in this area, pay close attention at upgrade time. Ideally this would be implemented as a WebComponent so that it was the same for both GDC and GWC and you could use same technique to customise for both.