How many times can I take the Battle Caster feat?
Once.
Alternatively, can something be both Feycrafted and Githcrafted?
Not a hope. You could have one or the other though, I suppose. However, extraplanar travel isn't common, even in the omni-racial trade city of Rivershire, so finding a Fey or Githyanki smith is difficult, and their goods are going to be quite rare, and accordingly costly.
EDIT: I'll review journals on Monday or Tuesday, to give everyone some time to actually write them... and there might not be a session next week, due to finals, I haven't decided yet.
EDIT
2: I read the description for blue ice. There aren't many deep, magical glaciers in the Civilized Lands, which means that to obtain this stuff, it has to be manufactured magically. As with all things magical, this is not a cheap process (you'll notice that according to the very basic Real Estate table found
here that you can buy a decent-size house for less than the cost of a +2 weapon). Blue Ice is going to cost 1.5x as much as stated in Frostburn. Also, I don't know about the Australians and Americans among us, but us Canadians know that wearing a suit made of ice is a rather stupid idea. In addition to the -1 initiative and reflex saves, wearing blue ice armor forces you to make a DC 12 fortitude save every 10 minutes you wear the armor, or take 1d4 nonlethal cold damage. If you fall unconscious due to this damage, all further damage taken from your armor becomes lethal.
Cold Resistance of at least 1, or an Endure Elements spell, will negate the initiative and reflex save penalties. Cold Resistance of at least 4, or Cold Immunity, allows you to wear this armor as comfortably as very light iron armor.
Note that this is a rather light penalty compared to what would happen to a real-life humanoid wearing a suit of ice. Hypothermia, stiff joints, reduction in your immune system's general capabilities... fun stuff. Anyway, Maelrigar, since we're in agreement that you shouldn't have been able to buy anything like the armor you've got, once you get to the Dwarf town, I'll give you a full refund on what you spent (4500 gp), and you can buy something else. Hopefully, we'll both have the presence of mind to double-check our math this time. Mutual derp.
EDIT
3:I apologize for the short session, and for the probable lack of session next week; it's that time of the university year. But once finals are over and the holidays kick in, I should once again be able to host your scheduled game.