The first step in treating a problem is positively identifying it. If you are seeing these pest plants in other areas of your lawn, and not just around the stump area of the removed tree, they are not sprouts from the old tree roots.
I would suggest contacting your state university extension, they have extensive fact-based knowledge of the plant problems and remedies for your specific area.
From your 1st photo, the 'rosette' looking plant on the lower left and upper right, resembles a common weed in areas of the Mid-Atlantic, Bull Thistle or maybe Canada Thistle.
If you check with your local extension agency (free service) they can tell you exactly what it is, and exactly what to do or use to rid your yard of it. That way you won't be spending money on some product that may or may not work.
Whatever product you use, it is very important that you follow the directions exactly, and read the entire label for safety, and optimal results.
They are nasty weeds!!
Wishing you the best of luck!
