You can be barred from entering other Urban Outfitters and if you decide to test this you can be charged with trespassing.
Yes. It is private property and there is no requirement that they allow you on it. If you were forbidden based upon race, religion, sexual orientation etc. That is one thing. However, forbidding you for suspected illegal activity is completely acceptable.
You can be barred. Many retailers now work with facial recognition equipment. Why would you even consider taking a chance by going into a retail establishment where you have been barred?