By David Mortensen, UC Berkeley
To be brief, Hmong as spoken by Hmong people in Southeast Asia, is a set of dialects of the Hmong language. That is, there isn't any other language of which Hmong is an “non-standard variety” or “dialect”.
To be prolix, this very common question cannot be answered without explaining a little bit of linguistic terminology. As used by linguists, the term dialect refers to any variety of a language whether it is “standard” or not. A language consists of a set of speech varieties (dialects) that are mutually intelligible (meaning that the speakers of the varieties can understand each other without being previously exposed to one another's way of speaking). The two Hmong dialects spoken by Hmong in the West Hmong Daw (White Hmong) and Mong Leng (Green Hmong) are part of a group of dialects called Western Hmong. Dialects of Western Hmong are spoken in pockets spread across southwestern China, northern Vietnam, much of Laos, and Northern Thailand. Hmong is not closely related to or mutually intelligible with any of the large national languages present in the area inhabited by the Hmong including Chinese, Vietnamese, Thai, and Lao. Western Hmong is closely related to the other Hmongic languages, and these are related in turn to Mien (another minority language of southern China and Southeast Asia). However, Hmong Daw and Mong Leng are only mutually intelligible with other Western Hmong dialects. As such, we can only say that Hmong is a dialect of Hmong.
The only proven relatives of Hmong are the other languages in a family western linguists call Hmong-Mien and Chinese linguists call Miao-Yao. This group consists wholly of minority languages spoken in Southern China and Southeast Asia. With the possible exception of Hmong and Mien, the list of languages in this family is populated with such obscure names as Hmu, Qo Xiong (or Ghao Xiong), Bunu, Pa-heng, She (or Ho-ne), Mun, and Biao Min.
But beyond this small group of relatively close relatives, the family affiliations of Hmong are unsure. Chinese linguists have long held that the Hmong-Mien languages, along with the Tai languages (like Thai, Lao, and Zhuang) are related to Chinese. It is true that all Hmong-Mien languages share a large number of words with Chinese, but much of this shared vocabulary can be shown to be the result of borrowing. If these Hmong-Mien languages are related to Chinese, the relationship must be a very distant one. Few scholars outside of China would defend this hypothesis. Certain Western scholars have attempted to show that Hmong-Mien languages are related to either Tai languages and Austronesian languages, or to Mon-Khmer languages (like Vietnamese and Cambodian). The evidence for all of these proposals is currently quite weak.
No. Or more precisely, there is no evidence to suggest that Hmong is related to Mongolian or any other Altaic language.
There are at least four writing systems used by substantial numbers of individuals to write Hmong: