"Sorry! No worries!"
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对 - 面对 To face (sb.)
不 - Not
起 - Capable (in this form)
我买不起法拉利 / I cannot afford a Ferrari.
So 对不起 means I cannot face you. (Well, no one really mean it when they say it.)
没 - No
关系 - Relation
没(有)关系 means sth. has no relation to my interests; It doesn't matter.
No. "别担心" is used when the listener is anticipating that something might go wrong in the future, or that they might receive some bad news.
"没关系" and "No worries" are used when the circumstances are already known and the speaker is reassuring the listener that no trouble has been caused, which is why they can be used in response to "对不起"/"Sorry".