Regarding some words and phrases.
There are some words and phrases in the course that I am a bit confused about. For instance, the character 谁 is pronounced "shei2". It was my understanding that this is an informal way of pronouncing the character and that a more formal way of reading it is "shui2" . Secondly, I had learned that the Chinese words for "here", "there", and "where" were 这里, 那里, and 哪里, which are erhua'd to 这儿, 那儿, and 哪儿. Are the erhua forms more common? Lastly, the word 牛 is pronounced /nju/. It was my understanding that is was pronounced /ni̯oʊ̯/. Could anyone shed light on these topics? Thank you in advance.
I can confirm that you are correct about the first two statements. I can't read IPA so all I can say about the last statement is that the pinyin for 牛 is niú and I'm not aware that it's irregular in any way.
Accents. Northerners of China (tend to) pronounce 谁 shéi, 这 zhèi, 那 nèi. While some southerners (Cantonese, one of the representatives) prefer the pronunciation 谁 shuí, 这 zhè, 那 nà.
I can't tell which are more standard. Dictionaries say zhèi and nèi are oral pronunciation, while shéi seems to have become as formal as shuí now.
EDIT: deleted wrong statements about 牛
You can consider zhèi as a liaison of 这 and 一, which also explains many grammatical issues on the usage of zhèi. Same to 那 nèi.