Hi,
When we'll be able to view Auction House status for each server online on Lodestone and Libra App (iPhone/Android)? It could mimic the in-game GUI for searching for items, checking stock and prices and viewing purchase history.

It's nothing new for MMORPGs these days. Even FFXI had www.ffxiah.com , albeit unofficial. Personally I've found it very handy.
Oh, and there is even an online shout/yell feed from FFXI main cities, you could add that too. But that would be low priority for me personally until you start curbing RMT spam.

You could provide some API too so that folks at http://www.ffxivpro.com/ can plug into some of that data too.