Arrow boot? I've been making and shooting wood arrows for a ong time and I've not heard of the "boot". Crown, maybe? The crown is a different color area, usually paint but sometimes stain or bare on the upper end of the shaft by the fletching. The crest is a series of colored stripes and fine lines originally used to identify a shooter's arrows but now commonly used for decoration. I'll add a pic at the end.
Parallel shafts are the same diameter from one end to the other. 5/16, 11/32 amd 23/64 inch are the common diameter shafts for adults. This is the most common shaft and works very well.
Tapered generally means "bobtailed", where the rear end of the shaft is tapered slightly for the last 9-10 inches or so. Normally 11/32 or 32/64" shafts will be tapered to 5/16" at the nock. To my eye and target, tapered arrows shoot better and I taper all of my arrows except maybe stumpers and squirrel arrows. The taper lightens the back of the arrow, moving the center of gravity forward (you will hear the term "FOC" quite a bit), and allow the arrow to recover from flexing around the riser a bit quicker. I also believe it somewhat "tillers" the arrow making it flex more evenly, much like the taper in a fishing rod or a bow limb. It's all theory, but it works for me.
Barrel tapered shafts are tapered on both ends. The descriptions of how much taper varies, but I figure barrel tapers are fairly symetrical, the brested taper is a longer taper on the front, and the more common "hunter" taper is a regular taper on the back of a 23/64" shaft with a shorter taper to 11/32" on the front, mostly to make the broadheads fit better. I have a machine set up for it and will do the hunter taper on request.
I use and recommend the tapered shaft. If you get into the higher spines and use 23/64" shafts, the hunter taper is worth considering for broadhead arrows. POC is a fine arrow wood, but Douglas Fir has been my favorite for many years. It's tougher, has good mass for a hunting arrow and IMO is the best shooting of the arrow woods.