TSNE interpreration and separability

I have a binary classification problem where I train a neural network on a training and validation data sets. But I am not satisfied with the performance of my trained classifier (the NN above). The loss function (a binary cross entropy) did not get lower than 0.1280 the on validation set and on the test set it is about 0.1340. I tried to somehow debug my data with a TSNE to visualize how separable my training data is.

My question is,

• can a TSNE visualisation give a feel of how much my data is separable and allow me to predict the performance of a classifier? It is clear from the image above that my data is not linearly separable but what else does it say about my data.

• Do you have any idea about how to improve separability?