Nearly all taxi drivers in Korea are men, and Korean men are quite comfortable being quiet when with others. Many foreigners can become uncomfortable in extended periods with no one making small talk. Korea is different, so please try to understand if the taxi driver doesn't talk much.
There are two kinds of Korean roads. One kind is broad and modern, with lines and traffic lights together with rules similar to those in other modern countries. But then there are the old style roads too, where modern rules of driving and parking can not always apply. Foreigners can sometimes be distraught by driving techniques in Korea, but understanding the two different kinds of roads here can help facilitate understanding.
Sometimes Korean taxi drivers hurry because it can be considered good service here to do so. It is possible that some foreigners might interpret this negatively, but please try not too.