It is possible to improve the graphics further beyond what is allowed by editing the "Background resolution" registry setting. For more details, see http://wiki.ffxiclopedia.org/wiki/Graphics#Background_Resolution
There are various 3rd-party tools used to improve the UI.
The normal way to change draw distance is the /localsettings command in-game. It is possible to increase the draw distance beyond the max using this Windower plugin: http://wiki.windower.net/plugins/drawdistance
This can be changed by using the /localsettings command. Syntax: /localsettings charanum [number] (25-50)
The max frame rate for the game is 30 FPS. If you are not finding your frame rate near that, it can help to turn off shadows in the in-game options.
Also try removing all USB devices. In the past, it was found that certain USB devices would cause a frame rate drop.
The game typically does not stay open if another program is in fullscreen mode. If something opens in fullscreen mode, FFXI will most likely close/crash.
Download the updated client.