Move your question to the Unity section, this is the editor section.

keshavsharma23 a écrit

1. How I play a animation exactly once in runtime.
   Explanation:- in unity, If I disable a Animator GameObject and then enabled it again, it plays the first animation once each time, if looping is turned off,

I'm not sure I understand the "Explanation" part above. It also ends with a comma, so perhaps there is some part missing? If you want to play an animation once using a SkeletonGraphic component, you can set Starting loop to false, then it will play the animation once and then stop. It will also not play it again when disabling and re-enabling the GameObject.

In general the components Starting Animation and Starting loop properties are just a very limited "beginner" interface. For more complex logic please check out the respective spine-unity documentation section:
spine-unity Runtime Documentation: Setting Animations
Layer you may want to check out the Spine-API reference:
AnimationState Methods

Also, please be sure to check out the example scenes in the Spine Examples directory that demonstrate usage of many basic features of the spine-unity runtime. You can also find a short documentation about the getting started scenes here:
spine-unity Runtime Documentation: Example Scenes

keshavsharma23 a écrit

2. Is it a must to keep skeletongrahics GameObject active before Play in unity to load/work?

No. You can enable and disable the respective GameObject whenever you like.