Chinese equivalent of "no worries"
Although not a direct translation, &quot;沒關係/没关系&quot; or  &quot;沒問題/没问题&quot; can also sometimes mean &quot;don't worry&quot; depending on context.

沒關係/没关系 - It doesn't matter (note: not suitable for the 2nd example)
沒問題/没问题 - No problems (ok for both examples)