For non-linear data, you can use a tree based algorithm such as Random Forests for feature selection. Read the "Random forests" section in this article to learn more about this. For your second question, you can use "Backward Elimination", "Forward Selection" and ''Random forests'' for feature selection. Here, dimensionality reduction happens automatically while selecting the best features! All the methods have now been included in this article. So, please read them. You cannot use other methods like PCA, LDA, t-SNE for feature selection. Those methods find a combination of new features instead of feature selection.