Visualizing k-means and hierarchical clustering for multiclass dataset - python

I have implemented code for analysing k-means clustering and hierarchical clustering on the following student performance dataset, but have trouble visualising the plots for the clusters.
Since this is a multiclassification dataset, PCA does not work on it, and I am not aware of an alternate method or workaround it.
Dataset link:
https://archive.ics.uci.edu/ml/datasets/Student+Performance

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If you are looking for some tutorial with dataset and python code examples, here you will find some examples.
Keras & Sklearn for binary (cat or dog) clustering.
https://towardsdatascience.com/image-clustering-using-k-means-4a78478d2b83
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https://towardsdatascience.com/how-to-cluster-images-based-on-visual-similarity-cd6e7209fe34

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I want to perform clustering on time-series data. I use Python's Sklearn library for the project. At first, I created a distance matrix by using dynamic time warping (DTW). Then I clustered the data using OPTICS function in sklearn like this:
clustering = OPTICS(min_samples=3, max_eps=0.7, cluster_method='dbscan', metric="precomputed").fit(distance_matrix)
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mds = MDS(n_components=2, dissimilarity="precomputed").fit(distance_matrix)
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The dark blue points are the outliers and the other two are the clusters identified by optics. I cannot understand these results. The yellow points cluster doesn't make any sense. I played with numbers and changed them but it always gives strange results. This is the same when I use DBSCAN but for K-MEANS and AGNES, I get more reasonable clusters when I visualize them. Am I doing something wrong here?

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Is there any way to measure the performance of algorithm?
Secondly, I have the labels of data and I want to test the learned model with the test dataset but I am not sure the labels Kmeans algo gave to cluster coincide with the labels I have.

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If you even just read the Wikipedia article on clustering, there is a section on evaluation, including supervised as well as unsupervised evaluation. But the results of such evaluation can be very misleading...
Bear on mind that if you have labeled data, supervised methods should always outperform unsupervised methods that do not have the labels: they don't know what to look for - there is lie reason to believe that every clustering happens to align with some labels. In particular, on most data there will be many reasonable clusterings that capture different aspects of your data.

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