Ah, sounds like you are the poster-child for the load issue in the client.
I don't think Yoshi has directly acknowledged this issue, but it's related to a low level defect in the client that causes a race condition in the dynamic loading of objects.
Basically, you should see signs of the crash is about to happen by a studdering in the game. You will not always see or get the studder of an object not loading in sync, as the first time it may crash things out.
The last pic you posted looks like you were trying to craft in a high traffic area. If your system is having issues with things like that, you might want to drop your render settings down a bit.
Really, this is just a design flaw (of epic proportions) in the current client. It has gotten better (when Ifrit was first introduced, almost every pt I was in had someone DC either entering the fight, or at some point in the fight, now I can go through a good 5-10 ifrit fights w/o someone DCing). Spell casting, and running around the Adv Guild, Crystal, and Repair person in Ul'dah are some of the worst areas for this as well. Simply running around there can cause an instant crash (or crafting or trading in the area).
I would recommend drop your settings a notch.
When you notice things are not loading, stop, and wait for them to load (specifically in towns, or very active camps), and, turn your camera away from mages when you can (sounds silly, but will cut down on the effects rendering, and reduce the chance of the cast).