In this dialogue, why does 一米八几 mean "more than 180cm tall"?
一米八几 means 1.8 x meters, where x is usually between 1 and 9. So the person's height is between 1.81 meters and 1.89 meters.

Therefore for your first question, 几 stands for some number that the speaker can not provide an exact value.

For your second question, the translation by google is not quite correct.

And for your last question, the meaning a few is what is being used in this sentence.