The rule is actually pretty straightforward. If applied loads are much higher than gravity load then gravity can be ignored in the simulation. In other case you should include it. However a good practice is to always apply gravity load in case of large structures. Especially that its application in FEA programs is very simple and it shouldn’t cause any problems with convergence or increased computational cost.
Is the gravity applied in terms of acceleration? I have an airframe and one of the conditions involves a vertical acceleration of 2.25 g. Do I have to apply 2.25 the acceleration for GRAVITY?
Also, every material has its density defines. Do I have to define the weight of the structure of it's implicit?
You can apply 2.25g using gravity load. Just multiply gravitational acceleration by 2.25 and enter the value in the appropriate Component term (depending on the orientation of coordinate system). When you define gravity load and specify material density then there's no need to input mass directly since Abaqus will calculate it using volume and density.