I don't understand when manages and mange are appropriate to use with what. This rule seems to change a bit in these lessons. I thought that with il/Elle/ on manges was to be used as the conjunction and with tu and je Mange was the conjugate. So why with La Fille is it not manges?
"manges" is only for "tu". "mange" is for "el/elle/je". Here's a nice reference for the conjugations: http://french.about.com/od/grammar/a/erverbs_regular.htm
Yes, it's "ree".
You only have to train your way to pronounce the French "r".
In the audio the "ee" sound is a bit too short, it makes it more difficult to understand for beginners (but not for native), maybe they could improve that, but I think they have to improve first the wrong audios (wrong liaisons, etc...)