Why is FBX readonly in animation editor when imported?

You have to duplicate the animationclip-asset. Select the animation clip in your imported model and press ctrl+d. Now you should have a seperate AnimationClip file. This animation clip have to be added to an instance of your model. Just drag your model asset into the scene and replace the referenced AnimationClip in the animation array. After you added the AnimationClip to your model you can open the animation editor window and select your model in the hierarchy. Select the right animation on top (if there are multiple) and you can edit anything in this animation. All changes will be saved to the .anim file since that's the animation you're using now.

You can't replace the AnimationClip on the imported model itself but you can create a new prefab out of the instanciated model in your scene. This prefab will used the assigned AnimationClip.

I have created a special AssetPostProcessor which automatically extracts the .anim files and add them automatically to the model prefab since we have 90+ animations ;)

edit

I've created a small test scene with your model:

AnimationEventsTest.unitypackage

All I've done is:

Draged the model into the scene
Created a new prefab ("Unit_Prefab")
Draged the model onto the prefab to store the model in the prefab
Assigned the seperate AnimationClips("moverun1.anim", "idlefiring1.anim") to the animation array on the new prefab.
Added my test script to provide a function for the AnimationEvent.
Select the model in the scene and open the animation window.
Added two AnimationEvents for the run animation.
Your idle_firing animation seems to be empty, but the run animation works. Oh and i cleaned up unnecessary/duplicated textures. All the animation-fbx files doesn't need to have a material / texture. Unity just need the AnimationClip. Actually after you duplicated the AnimationClip you could completely remove the animation-fbx files. Only when you want to update your animation you have to reimport the animation and duplicate the Clip again.

Because of that procedure we created a specialized AssetPostProcessor which does this steps automatically. If you need to do this 90+ times it's no fun ;)

Link: http://answers.unity3d.com/questions/187907/how-to-add-keyframes-on-imported-read-only-animati.html