Basically, the 5.56/.223 are the same cartridge and .223 reloading dies handle reloading 5.56.
5.56 is more of a chamber specification than anything to do with the brass.
As with all brass...measure and correct before reloading. Such as, size and/or trim to correct length before each reload.
I have been using Lee Precision die sets with the additional "Factory Crimp Die" (pistol and rifle). Since my firearms are auto loaders, the FCD ensures my rounds will chamber. Some rifle die sets have a neck sizing die for chamber sized brass (brass fired in your rifle chamber). For an AR, you most likely will be using a full size die (to size and decap), seat and crimp die, followed by the FCD to make rounds that should fit any firearm of that caliber.
For the brass, check condition, clean, ream primer pockets if needed to clear military crimp (can just chamfer with a case mouth tool to remove the sharp crimp edge...or use an expensive purpose swage die/tool) and run through resize die to decap and size. Measure length and determine if trimming is needed (cases can and often do stretch in length from being fired). It is not so much of a problem with fitting the mag as it is fitting the chamber.
Answers to questions:
1. Yes, use .223 die set.
2. Load per the .223 die set. I loading for accuracy, sort out bullet to rifling distance (most likely after sifting through a number of internet reloading forums). It seems distance the bullet travels before hitting the barrel rifling can influnce performance.
3. Main concerns will be condition and your processing to reload.
4. As per above. Main consideration will be sizing brass to chamber automatically. A factory crimp type die takes care auto chambering. The round will be looser than a chamber sized brass and accuracy will not be like a chamber sized brass in a bolt gun. You trade off a little accuracy for firing speed.
