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Undiluted Round-up will help kill the surviving roots. You will need to wound the roots/shoots (normally, people cut the suckers down and use those wounds) and then paint the undiluted Round-up on these wounds. The bigger or more wounds you paint, the better. The roots will suck the Round-up in and it will eventually kill them. You may have to repeat the process a few times to fully kill the roots if the root system is still strong. This article should also help with removing the stump: https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-stump-removal.htm

I would suggest calling in a professional to remove the tree.

https://www.gardeningknowhow.com/ornamental/trees/chinaberry/chinaberry-tree-information.htm

The seeds from the Chinaberry Tree are very easy to germinate.
When the fruit drops to the ground the hard seeds can be collected.
They can be started in small pots of a good quality potting soil.

https://www.gardeningknowhow.com/ornamental/trees/chinaberry/chinaberry-tree-information.htm

Yes, they can be grown from the seed inside the mature berry. The seed is mature when the berry falls from the tree. You can plant the seed directly in the ground or start it in a pot and then transplant the seedling. The seeds tend to germinate well, so it should be straightforward to get them to grow.
https://www.gardeningknowhow.com/ornamental/trees/chinaberry/chinaberry-tree-information.htm

Yes! This tree is the source of Neem oil, which is a clean burning oil. This makes it an excellent tree for firewood. Here is an article for more information: http://aggie-horticulture.tamu.edu/plantanswers/trees/neem.html

If you can wait until winter for transplanting they will be more likely to survive a move during their dormant period in cooler weather. If you have to move them now, dig them up with plenty of soil in a "root ball". Water right away after moving and then every day until you see some new growth happening. Then water a couple of times a week until they lose their leaves for winter.