Sorry in advance if someone already posted this but here is a new harp trailer: http://www.zeldadungeon.net/2011/10/skyward-sword-harp-trailer/#comments
Is the spelling Fi confirmed? I know that's the way we've seen it lately, but has Nintendo said that is definitely the spelling? If so, I'm kinda disappointed. Phi just looks much better...
That dungeon Link walks out of is probably in the desert, as evidenced by the hills. Most likely you get the harp at that point during the third dungeon plot twist, Zelda is taken by Ghirahim, and Link must restore power to both the Goddess Sword (into Master Sword) and Harp (adding songs/using it to activate things).