Yes there were agile co workers who worked from home sometimes.
Yes the hours are flexible and working from home is definitely an option
Role dependant, and work from home days are up to the manager's discression. Most departments are comfortable with a day from home, if the role meets the proper criteria.
Flex hours are common, most departments expect communication when flex time is used, and that core hours are not being affected.
Yes there are some depend on your position
Yes; company is moving towards a flex-space environment due to not enough cubicles/workstations within their offices.