If it in a mall or a plaza but if it is a general public downtown area, is that right?
As long as you don't use physical violence and the property is yours then yes you certainly can. Or call the police on them.
In some jurisdictions yes, check you city ordinances. Some cities have a aggressive panhandling law, and some don't. Aggressive panhandling is if the person actually asks for money. If a person is sitting on the sidewalk and not impeding traffic, and has a cup then he is not being aggressive and it is legal in some places.