You never register CapabilityHandler on the Forge event bus, so CapabiltiyHandler#attachCapability is never called and the capability is never attached to any ItemStack.
What diesieben07 said also applies, though.
This is what the sided proxy system is for. Create a method in your base proxy class called something like registerModel and then override it in the client proxy to call ModelLoader.setCustomModelResourceLocation.
Keep in mind that ModelResourceLocation is also a client-only class, so you can't have it as a parameter of the method. Instead, you'll need to have the name as a parameter and create the ModelResourceLocation in the client proxy's override method.
You can read more on sides here.
Only use AttachCapabilitiesEvent to attach capabilities to external objects.
For your own Items, override Item#initCapabilities to return a new instance of an ICapabilityProvider implementation that provides the capability instance.
Your ICapabilityProvider should store the IItemHandler instance, implement ICapabilityProvider#hasCapability to return true if the Capability argument is CapabilityItemHandler.ITEM_HANDLER_CAPABILITY and implement ICapabilityProvider#getCapability to return the IItemHandler instance if the Capability argument is CapabilityItemHandler.ITEM_HANDLER_CAPABILITY.
If you installed using the installer, and used vanilla mojang launcher it'll work.
But a few things to note:
1) 1.7.10 isn't actively supported here anymore, you should update to a modern version they are a lot better.
2) You can copy/paste that text, instead of posting screen shots, it's far more helpful as it's less of a pain for us to read. Esp if it's large amounts of text.
Hi
These links will tell you more about mining speed of blocks than you ever knew you didn't want to know.
http://greyminecraftcoder.blogspot.ch/2015/01/mining-blocks-with-tools.html
http://greyminecraftcoder.blogspot.ch/2015/01/summary-of-logic-flow-when-mining-blocks.html
http://greyminecraftcoder.blogspot.ch/2015/01/calculating-rate-of-damage-when-mining.html
-TGG