Time series clustering using dynamic time warping and agglomerative clustering
Visually, there are no clusters in your data.

If your data had clusters, there would be subtrees with a small MRCA, with a long line leading to it.

There are metrics to quantity this, but you are not there yet. Can you show the time series? (or better, send them to me)

You may be lucky, and have one of ten problems that are easy to fix. See this paper.

You ask " when is z-normalising not required for DTW?" The answer is never.
eamonn