If you cant lower that draw length, it will be a problem. Especially if you shoot a release.
Yes, you can shoot carbon arrows. Or aluminum. Don't try wood arrows in a compound though. You need AT LEAST 5 GRAINS PER INCH FOR EACH POUND OF DRAW WEIGHT. This means a 50 pound draw weight would need to shoot an arrow weighing at least 250 grains. That is still way to light in my book. Shoot a heavier arrow and use 100-125 grain broad heads to hunt with. Add the weight of the arrow plus weight of the head-field tip or broad head to figure total weight.
Yes, just start with field points first. Worry about your broad heads later.
If you have an archery shop any where near you, I would strongly suggest stopping by and talking to some one there. Pretty much any who is in to archery would be more than willing to help you out.
Welcome to the addiction!