k-means is rather sensitive to noise in the data set. It works best when you remove the outliers beforehand.
No. Any cluster analysis algorithm that claims to be parameter-free usually is heavily restricted, and often has hidden parameters - a common parameter is the distance function, for example. Any flexible cluster analysis algorithm will at least accept a custom distance function.
one-class classifiers are a popular machine-learning approach to outlier detection. However, supervised approaches aren't always appropriate for detecting _previously_unseen_ objects. Plus, they can overfit when the data already contains outliers.
Every approach has its pros and cons, that is why they exist. In a real setting, you will have to try most of them to see what works for your data and setting. It's why outlier detection is called knowledge discovery - you have to explore if you want to discover something new ...
