Getting a best k in KNN Algorithm
Looking into the linked answer, it appears that they are directly training on X and y since they're using a GridSearchCV, which already includes a k-fold cross validation (5 fold by default). So basically you'll already have a score for the classifier by calling GridSearchCV with the defined pipeline.

That being said I'd argue that it is never really the recommended approach to directly do this without a final test step, to asses the performance of the trained model on unseen data. So even if you do a k-fold cross validation, it is advisable to leave a test set to get a final score, specially when the k-fold process involved a hyper-parameter tuning, as in this case. In such cases you  need anther validation step that is independent of the tuning.

And in relation to the second point, no, you don't need to include a StandardScaler if the data is already normalised. Though, since you're using pipeline, you might as well include all transformation logic in the pipeline, for the sake of simplicity.