Which order is correct Feature Selection then Outlier Detection or vice versa?
In majority of the cases feature selection should be done after outlier detection. Outlier detection should be done at the initial stage of data pre-processing while feature extraction / selection can be don in the last part of  data pre-processing.

Outlier must be detected beforehand so that actual behavior o that particular predictor is known. Then depending upon the behavior after removal of outlier it can be decided whether to keep that as feature or not.

Many feature selection algorithms like PCA, regression, etc are sensitive to outliers and so if such algorithms are used to extract the features then it would be better to remove the outliers beforehand.