Did you get your tree questions answered?
I am not sure exactly what the situation is with the plum tree. If it is sending up shoots from the
roots, I've always called those "suckers". If your tree was grafted, and most fruit trees are, then the root stock is what is sending up shoots, and, if you separated a nice healthy shoot with some roots and grew it, you could graft onto it.
Most fruit trees are vegetatively reproduced, whether by grafting, or by rooting cuttings. in essence, every single granny smith
apple tree has been grown from a piece of the original
apple tree in granny smith's garden. If you start from a seed, you will have a new variety. It might be wonderful, you could name it and patent it, or it might be bitter and awful.....
If you are wanting root stock, or to know about the qualities of the various rootstocks, Raintree Nursery www.raintreenursery.com/ is a great resource, and they don't just
sell root stock and conventional widely known and cultivated plants. They sell aronia and goumi and pawpaws. I don't know a better source for unconventional and odd ball food plants. Check them out!
Thekla