In order to kill a tree that size, you would get the best results cutting the tree down to a stump and treating the fresh cut stump directly. If the trunk diameter is less than 6-8 inches, then you could potentially do a basal bark treatment with Crossbow Specialty Herbicide.You would mix 1.25 to 5 ounces per gallon of solution, mixing in diesel No. 1 or 2 or kerosene, then spraying the basal part of the tree up to a height of 15-20 inches off the ground. If you do not need this much product, then could also use Fertilome Brush Killer and Stump Killer.
Tree of Heaven is an invasive species that can require chemical and cultural methods to control completely. You will probably need to cut a treat the stumps directly with a product like Crossbow Specialty Herbicide for best results. This article from the PennState Extension service has more information about this difficult tree.
Crossbow Herbicide is specifically designed to kill brush, vines, woody plants like trees, and broadleaf weeds without harming grasses when used at the labeled rates. It will not, however, kill or control moss as moss only grows in areas where you have too much moisture and poor soil conditions where the PH levels are off and the soil is too compacted. Renting a core aerator and running it through the area you have heavy moss concentrations will greatly help. If there are any tree branches keeping that area shaded that you can trim back or cut off then you will want to do this as well so you help keep the area dried out to prevent new moss regrowth. You can spray a moss control product like Lilly Miller Moss Out, however changing the conditions causing the moss is always the best way to go so that repeated sprays aren't necessary in the long run.
Crossbow Herbicide appears to be an effective product on salal but it can take mulitple applications. Best way is to either spray the foliage directly or cutting the stumps/sprouts and applying as a “cut stump” as directed on the product label.
It can take 2 plus weeks after Crossbow Herbicide application to see that plants are dying. You may reapply if needed 30 days after initial application.
It is recommended to mix and use Crossbow Herbicide is a hand pump or backpack sprayer. We typically recommend the Chapin Premier sprayer or the Chapin Backpack sprayer.
Crossbow Herbicide does contain an active ingredient that has soil residual. Per the product label: "This chemical has properties and characteristics associated with chemicals detected in groundwater. The use of this chemical in areas where soils are permeable, particularly where the water table is shallow, may result in groundwater contamination."
If you are applying the product as directed to apply to fresh cut stumps, then there should not be a risk of contamination in most circumstances. However, this product is not labeled for use around aquatic areas or where there is risk of flooding.
Per the Crossbow product label: To prevent or control regrowth from cut stumps, mix 4 gallons of Crossbow in diesel oil, No 1 or No 2 fuel oil, or kerosent to make 100 gallons of spray mixture. This breaks down to about 5.12 oz of Crossbow per gallon.
Crossbow Herbicide is primarily designed to control weeds and woody brush type plants and vines from unwanted areas but is designed to not harm most grasses. There are some grasses it will control listed on the label but its primary focus is to not harm grasses. You may want to look at using something like Roundup QuikPro for the weed in your driveway or possibly a soil sterilizer like Pramitol provided careful application is used to ensure no damage to surrounding desirable plants like trees, flowers, and the lawn.