It depends on the type of irregularity. The most common is called a slub. Slubs are short sections of the yarn that are wider than the areas on either side and are either not twisted or not twisted as much as the rest of the yarn.
There are also snarls, knops and other irregularities that can be intentionally added for artistic effect.
A condition someone is born with is called congenital.
Congenital anomaly
the fabric weave by dyed yarn called yarn dyed fabric
Individual fibers are spun into yarn.
Yes, a small amount of wool yarn can be called a skein, especially if the fibre is rare and expensive, such as baby yak wool yarn.
Wool.
Wool
The plural form of irregularity is irregularities.
Loopy yarn can be yarn with loopsembeddedin the yarn lengths.
If they do, it's a rare disorder called "pica".
A coil of yarn may be called a hank or a skein. Yarn is typically sold in a ball or a skein. A hank is different in that it is a big loop of yarn that is twisted up for easy shipping.
Yarn that is a single strand is called single-ply or one-ply.