I don't know if you got help with this yet, but I would suggest you have a certified arborist do the initial pruning for you and observe closely where and how they make the cuts. I also see several branches that appear to be growing into the center of the crown. Not more then 15% of live branches should be pruned each year. The best time to prune a maple is May and June.
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.