Steel pipe comes in 21' threaded pipe joints. The pipe has NPT threads on both ends and a coupler on one end making a full joint mipt x fipt overall. Cut lengths won't include a coupler; if you need one, you should order one.
Nipples are short lengths of pipe which have NPT threads on both ends (mipt x mipt) that fit any female iron-pipe-size threaded fitting of the same diameter. An "All thread" nipple is used for tightening two fittings together in the shortest possible length. There is no place to apply a pipe wrench directly onto an "all thread" nipple.
Yes, the very popular 1/2" and 3/4" sizes usually cost less than even smaller diameters.
This is because there are economic and production factors involved that make more difference than raw material and weight.
Before final assembly, the installer must remove the coupler and apply an appropriate joint compound.