Yeah, item distribution in CW is much more balanced.
Some very good items are non random too, i guess one of the is crown of chaos, i don't know why that item always in all my games.
Usually the non random one is in nameless island. Yeah i often get 2 crown of chaos, if i remembered right, by choosing rakush i can get 95% astral resistance
Yeah, most of the time, i named my pet dragon with the same name, however in some of my games i changed his name, but the heart of the dragon often spawn, sometimes the eye of the dragon that spawn in arnold.
Eventus often sell heart of dragon though. Warrior can have 44 red dragons with both of those + drakonix, and if i remembered right that is without +leadership item, though i use flaming eyes.
As for composite, i never complete them except dragon toys (once), and scrounger ring (twice). Some of the composite is indeed very powerful, like the belt, however that is still not my top item, i'd still prefer +resistances item than that or -leadership item.
As for the banner and name tag, probably yes or probably not, the only way to know is by looking at how the algorithm randomize them.