What is the Deal with "Erhua"？

One of the most salient features of Beijing Dialect (北京话）is that of  "Erhua" (儿化）， adding 儿sound after a noun. Function wise, there are 3 types of Erhua:
1. To change meaning. 
While 头 and 头儿 both are noun， 头 means “head” the body part whereas “头儿” means “head ” of a department， school or any organization. Ex. 学校的头儿是校长。
白面 means “white powder”  while 白面儿 means “heroin”
2. To change part of speech
While 画 is a verb meaning  “draw；paint” ， 画儿 is a noun meaning “drawing；painting”
While 尖 is an adjective meaning  “sharp” ， 尖儿 is a noun meaning “sharp top part” . Ex.  笔尖儿
3. To make small things more adorable and dearer
小孩儿， 门儿 （door， not gate， gate is 门）， 宝贝儿

There are 3 main ways 儿化 would change pronunciation
1. When there is no coda for the preceding character， simply add “r” 。 Ex. hua'r 花儿，zhe'r 这儿
2. When the preceding character's ending is "ai" "ei" "an" “in” or "en". Eliminate the ending and then add "r". Ex. hái 孩- há'r 孩儿；jīn 今- jī'r 今儿； míng明 -mí'r (sounds like 米儿）
3. zhi， chi， shi becomes zh'er, ch'er sh'er.  Ex shì 事 -sh'èr 事儿。zhí 侄 - zh'ér 侄儿；