Omotola-here are a few comments:
1: If both curves are presented in the same matrix i.e. limestone and you are dealing with a single primary porosity system then the answer is yes it can be an indication of no near wellbore gas. You have to be careful though as gas has a higher mobility than invading fluids such that the mud filtrate can move enough gas away from the reservoir so that it is beyond the depth of investigation of the tools so, there can still be gas present but you wont see it on neutron-sonic plot.
2: Sonic tools will respond to primary porosity due to fluid filled fractures or vugs not supporting the shear component. Comparing total porosity from a density neutron crossplot to sonic porosity can give you a secondary porosity index.
3:There are a lot of variables here. If you are in a field where you have a good idea what response is indicating producible saturations then yes. For a wildcat you need detailed calculations, which the tools you mentioned would be adequate for, unless you are in a known trend where a visual would give you confidence in making a depleted call. I am assuming you also mean water displacement in depleted. If the reservoir is pure volumetric then you need pressure data. If it is a single phase volumetric gas reservoir then the lack of gas response on conventional logs can indicate pressure depletion.
Hope this helps