zhōng wén (中文) is used when the opposite may be English, Japanese, etc., whereas "pǔ tōng huà" is used when the opposite may be other Chinese dialects. Like in most countries, the most standard Chinese dialect can be found on television. In China, all the TV anchors are required to speak standard pǔ tōng huà (普通话). hàn yǔ (汉语) – Mandarin. hàn refers to hànzú (汉族) , or the Han ethnic group. Of the 56 ethnic groups in China, the Han people account for over 90% of the population. hàn yǔ (汉语), as the name suggests, refers to the language of the Han ethnic group, or Mandarin. Mandarin Chinese is considered “standard” Chinese -- as opposed to other Chinese dialects. pǔ tōng huà (普通话) and hàn yǔ (汉语) and are pretty much the same thing. You can think of pǔ tōng huà (普通话) as the more standard, better-pronounced hàn yǔ (汉语). And I think you can say： wò shì xué（learn） putonghua de xué shēng.

it's not xueshen, it's xuesheng, with g you cannot use nǐ-hǎo addressing to many people you should use nǐ-men-hǎo because you are saying "I'm the student of commonspoken language" but commonspoken isn't how it's called because it's called either Zhong-wen or Han-yu and commonspoken is rather a description * there is always why for everything * the difference between "Castilian" and "Spanish" is exactly the difference between "Cantonese" and "Chinese"

because there is no specialty named putonghua

Xièxie

Because in China not all places say mandarin.But all Chinese can say Chinese.And you should pay attention to it is xuesheng（学生），not xueshen！