Is the statement "One can always use PCA wherever SVD is used for dimensionality reduction" true or false?

The eigenvector corresponding to the largest eigenvalue points in the direction of the:

Applying PCA is beneficial when the non-diagonal terms of the covariance matrix are zero or close to zero. True or false?

While applying PCS, the class labels if associated with the data are ignored. True or false?

You are working with a data set consisting of five features. To apply PCA, you calculate the covariance matrix and get the five eigenvalues as 18.67, 12.50, 2.25, 1.05, and 0.75. You want to achieve as much as dimensionality reduction that is possible to keep the mean square error (mse) below 2.5. What are the eigenvalues that you will select?

Given a single gray level image of size 32x32, is it possible to approximate it via SVD?

You have two buckets of red and blue balls. The first bucket has more red balls while the second bucket has equal number of red and blue balls. Which bucket is associated with more entropy?

You have two distributions. A friend of yours calculates the KL divergence measure for them and obtains a value close to zero. What conclusion can you draw from this result?

Mark the nonlinear method from the list below for dimensionality reduction.