Does the TouchBar have its own GPU, CPU, or Ram? I want to know if the touch bar uses a miniature iOS-style CPU and processor, or does it share CPU, GPU, and other aspects with the main computer?

Can I (in theory) offload tasks (GPU/CPU,etc) to the touch bar?
This answer may not get to the crux of what you're wanting to do, but I offer it because I think your question is one that will interest a lot of people.

Apple’s Touch Bar MBP models actually use an Apple designed T1 chip that helps power both the Touch Bar and the Touch ID sensor. I say helps because this works in conjunction with the Intel CPU at the core of the MBPs. This T1 chip is actually the same that sits within the S2 in the current Series 2 Apple Watch models (it's being used as the processor and the Secure Enclave1).

During Apple's keynote it was revealed that in addition to being used for the Touch Bar, the T1 also handles security for the Touch ID sensor, the camera, and the keychain.

In terms of the Touch Bar, while the T1 does the sending of pixels to it, the main Intel processor is what actually renders the content that the T1 sends across. 

In terms of security, the T1 is responsible for rendering any Apple Pay dialogs (because it's able to leverage off the Secure Enclave) while the actual transmission of any Apple Pay data is actioned by the main Intel processor.

In terms of what you want to do (i.e. offloading tasks to the T1), I'm not sure if/how this would work as I've only done iOS development. However, I do know that developing anything for the Touch Bar requires a Mac running macOS Sierra and Xcode 8.1 or above. Below are some resources that may be of interest:


Human Interface Guidelines for the Touch Bar
NSTouchBar
NSTouchBar Catalog: Creating and Customizing NSTouchBar


1. The Secure Enclave is a segregated portion of the chip used for personal information - the same process used in iOS and Apple Watch devices. You can read more about this in the iOS Security Guide.