"Sorry! No worries!"
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.
but isn't what you translate here to literally be "to face" previously taught to translate to "correct"? and about the second sentence how can "mei" be "no" if "bu" is "no/not"? and you translate the latter two words to literally mean "relation" so does that mean they don't have individual translation? thanks a lot!
One word can have 2 or more meanings. It also happens in English, like Right as in right side and Right as in you are right and Right as in legal right. So why not in Chinese?
关系 is one word with two characters. It can be possible that each character is respectively a word by itself but the meaning may not be the same any more. When you learn a Chinese word it is necessary to learn them by the combination, just like you don't combine Grape and Fruit to get Grapefruit.
没 and 不 are two different forms of negation in Chinese, they both translate to No or Not depending on the case.