There are several plants called umbrella plant, but I suspect your plant is a variety of Schefflera.
Your plant is a tree and the only way to make it look fuller at the base would be to root cuttings and plant them as you have mentioned. You can prune newer growth that hasn't hardened bark and try and root that with a rooting hormone or by air layering.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.