Trees gave been in fir five years. Cool temperate climate. Garden in some shade but full sun in summer months.
One thing you can do is remove the grass under the tree 3 feet (0.9 meters) out and fill it with mulch. The grass is competing with the tree for nutrients, plus if you add nitrogen fertilizer to the grass, some may be getting to your tree. Mandarin trees can be fertilized with a citrus fertilizer according to the package directions.
If frost threatens, cover the tree with a blanket. Also be sure it is getting regular watering. Mandarin trees need well drained soil in full sun, so if the soil is not well draining, work in some compost around the tree.
Here is more:
https://www.gardeningknowhow.com/edible/fruits/tangerine/mandarin-orange-tree-care.htm
https://www.gardeningknowhow.com/edible/fruits/oranges/no-fruit-on-orange-trees.htm
https://www.gardeningknowhow.com/edible/fruits/oranges/dry-orange-fruit-why-an-orange-tree-produces-dry-oranges.htm
My question is that my ten-year-old Satsuma mandarin plant is dead but the rootstock is alive, I have checked this. Can I use that rootstock again now, I need your guy's guidance.
You can use it to graft another scion but it would not suffice as a tree itself.
https://www.gardeningknowhow.com/edible/fruits/tangerine/mandarin-orange-tree-care.htm
https://www.gardeningknowhow.com/garden-how-to/propagation/grafting/what-is-a-scion.htm
I intend to spray tree today with neem native insecticide
Yes, it is safe. Although terrible for your tree, it is harmless and peeling it will remove any doubt.
This article will go over several things that you must do to keep this at bay:
https://www.gardeningknowhow.com/plant-problems/disease/anthracnose-disease.htm