The photos indeed do show that to be Ailanthus altissima and it is definitely a female tree.
Here is the biology description of it.
Description and Biology
•Plant: deciduous tree that can reach 70 ft. in height; twigs with smooth, pale gray bark, and twigs that are light chestnut brown, especially in the dormant season; dioecious meaning plants are either male or female;
wood soft, weak, coarse-grained and creamy white to light brown in color; leaves, stems and some flowers have a strong, unpleasant to offensive odor likened to cat
urine or rotting peanuts or cashews.
•Leaves: alternate, large (1-4 ft. long), compound, with 11-25 smaller leaflets, each with one to several glandular teeth near the base.
•Flowers, fruits and seeds: large showy clusters of small yellowish-green flowers produced during June; in summer, flat, twisted, single-seeded winged fruits or samaras are produced on female
trees and may remain on trees for long periods of time; individual trees may produce an estimated 325,000 seeds per year.
•Spreads: reproduces by seed and by vigorous re-sprouting, especially in response to injury such as breakage or cutting.
•Look-alikes: compound-leaved shrubs and trees like staghorn sumac (Rhus typhina),
ash (Fraxinus sp.), black walnut (Juglans nigra), and hickory (Carya sp.). Sumac has fuzzy, reddish-brown stems and leaves; ash species have opposite leaves; ash, black walnut, hickory and sumac leaf margins are completely to mostly toothed; black walnuts have large green fruits.
It is considered Invasive and illegal to plant new ones. If you want to remove it, you would have to remove all soil in the area to insure getting all the roots since it can reproduce from a 2" segment of
root.
It reacts much like the sumac in that if you cut the tree down, the surviving roots will send up new shoots all along their length.
This make eradication only possible by completely removing all the supporting soil ( think crater digging ) so that all the root system is removed.
It is possible, but for folks like us ( permies ), it is best to leave alone, since to eradicate it requires large doses of Herbicides that are systemic.
You can possibly contain it but that will require a thick, deep barrier (something like 1/4 in. thick steel) that is buried 5 ft. deep all around, out side of the
drip line (you would have to contain all the root tips).
This is really economically unfeasible to do since you most likely would slice through some root tips even if you dug 30 feet out from the drip line of the tree, not to mention the cost of the barrier material.
