What time of year should I harvest the berries and how do I dry them?
The berries come from a seed pod that will burst when ready. This can be anywhere, usually, in December and November.
This article will give you information on the tree: https://www.gardeningknowhow.com/ornamental/trees/tallow/chinese-tallow-tree-info.htm
Dehydrating should be done in a dehydrator or drying rack until dry.