なんか is an expression in Japanese that is frequently associated with the 副助詞（ふくじょし） (adverbial particle)
など. They are thought to have overlapping meanings in many circumstances, and
なんか itself may be considered a 副助詞（ふくじょし）.
なんて is an extension of this, and may be considered an abbreviation of などという ‘to say something like’.
Both なんか and なんて are used in the same way as
など, having translations like ‘such as’, and ‘things like’ in English. The primary difference between なんか and なんて is that なんて is far more common after 用言（ようげん） (conjugatable words). This includes verbs,
い-Adjectives, and
な-Adjectives. On the other hand,
なんか is almost exclusively used after 体言（たいげん） (unconjugatable words). In other words, nouns.
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こんな嵐（あらし）の中（なか）走（はし）るなんて、頭（あたま）おかしいんじゃない。
You are going to do something like run in the storm? You must be crazy.
北海道（ほっかいどう）がこんなに寒（さむ）いなんておもわなかった。
I didn't think Hokkaido would be this cold or anything.
心配（しんぱい）なんてしている場合（ばあい）じゃない。
This is no time for things such as worrying.
テレビなんか叩（たた）けばだいたい直（なお）るだろ。
Things like TV’s will be fixed most of the time if you hit them, right?
Despite the 体言（たいげん） and 用言（ようげん） tendency, most native speakers will not consider it incorrect to use either
なんか or
なんて with any type of word.
Both
なんか and
なんて are often used to show a low evaluation of the word that they follow. This can come across as humility when used in relation to oneself, or as an insult when used in relation to others.
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私（わたし）なんか5年間（ねんかん）スペイン語（ご）の勉強（べんきょう）をしているのにまだ全然（ぜんぜん）会話（かいわ）ができないです。 (Humility)
I have studied Spanish for 5 years, but I can't speak it at all yet.
お前（まえ）なんてどうせ、家（いえ）でゴロゴロしているだけだろ。 (Insult)
Someone like you probably just loafs around the house, don't you?
Don’t let this point stop you from using
なんか or
なんて though, as many native speakers use it simply to fill the silence in modern Japanese.
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酷（ひど）いことを言（い）ったのは分（わ）かるんだけど、なんか、情熱的（じょうねつてき）になって言（い）っちゃった。
I am aware that I said something mean, but, you know, I said it because I got emotional.