I, personally, never have been able to see fbx objects imported from blender. I do not know if this is a blender issue or AppGameKit has problems with fbx.
As I have bought quite a few items from Unity that are fbx and they do not show up in AppGameKit or animate correctly. I have to export them as OBJ(if not animated) or DAE(if animated). In my experience, DAE does not export IK mechanics or any type of bone constraint( in my very uneducated opinion, this is due to Blender not AppGameKit ). You will have to do each of this manually. If you are able to export via fbx please do share a guide for the AppGameKit community. I would love to buy unity products and use them as is. Sadly, I have to use my pathetic skills to animate.. lol.
You have 276 bones in that screenshot... I think AppGameKit maxes at 100? I also see your model is 4 MB. Is that without any animations? That is pretty large.
Here is my test character that is less than 1MB. I have 36 bones and 180 animation frames ( my death animation needs work lol!! ). Animations frames can become very memory intensive. Again, my uneducated opinion is to make each "action" less than 10 frames. Unless, you're trying to make some type of AAA game on PC no one is going to notice.
A lot of the "old guard" of AppGameKit use .x. Sadly, there is little to no support to those of us who are the "younger guard". You know, we rely on youtube and google to learn. .x is outdated and no longer supported. I wish the big AppGameKit developers would move away from .x. That is not the way of the future.