〜など／なんか／なんて
Something like… (dismissive/exclamatory)machine translation
FormationNoun + など／なんか；noun／plain-form clause + なんて
Beyond the familiar listing meaning "and so on," など and its two colloquial variants なんか・なんて also BELITTLE what comes before them: "something like…, … of all things." 私の気持ちなんか誰にも分からない (as if anyone could understand feelings like mine) — self-deprecating; 旅行に行く時間などない (I don't even have time to travel) — dismissive.
なんて can also attach to a whole clause to express surprise, exclamation, or reproach about the event itself: 嘘をつくなんて、ひどい (lying — that's awful). This is where なんて is broader than なんか — なんか only follows nouns.
Note the nuance: used about yourself it's humble (私なんか), but used about someone else or something they treasure it's contemptuous — 先生の授業なんて is a sentence that will cause offense. こそ sits at the opposite pole: it elevates ("precisely") instead of putting down ("something like"). For hard-to-believe events, なんて pairs naturally with まさか in exclamations.
Examples
私の気持ちなんか、誰にも分かりません。
As if anyone could understand how I feel.
友達に嘘をつくなんて、ひどいです。
Lying to a friend — that's just awful.
忙しくて、旅行に行く時間などありません。
I'm so busy I don't even have time to go on a trip.