No, however the Commissioners Court may impose a fireworks ban under certain conditions..

Yes. Open flame cooking can be done outdoors during a burn ban, however the flames must be completely enclosed in the cooking device.
Read more about safely cooking outdoors.

Yes. however the Commissioners Court may require that certain procedures be followed during a burn ban. The Burn Ban Order will contain information about safety matters that must be addressed by individuals conducting hot work operations.

You may burn limbs, leaves and straw that originated on your property.

No, you would need to contact the Austin Fire Department for questions regarding burning inside the City of Austin. Their number is (512) 974-0130.

You would need to contact the park directly for their guidelines.
Travis County Parks website

Dial 911 In Case of an Emergency