

The motor cortex is located in about the same spot in everyone, to my knowledge - I don’t know of any reported exceptions. The pre-central gyrus. Within, motor neurons are organized in specific regions that control specific body parts. Again, I don’t know of any reported exceptions - my understanding is everyone’s motor cortex has the same organization. It’s known as the cortical homunculus. https://en.wikipedia.org/wiki/Cortical_homunculus#Motor_homunculus%3Fwprov=sfla1
So by reading output from a small group of neurons, yes, you could control a prosthetic limb. It’s been done a few times, actually! But, you typically need more precision than comes from an EEG electrode, so all the examples I can think of are using invasive electrodes.
In fact, the sensory system of the brain has a very similar organization - along the postcentral gyrus, and the same stereotyped organization within. If you could stimulate the correct region of the sensory cortex, you could create a prosthetic that allows you to feel.
There are some more technical limitations though - there’s different types of sensation (e.g., pain, temperature, proprioception (position in space), texture, etc.) that are controlled by different receptors in skin and have different wires connecting to the brain. You’d have to be very careful about what you stimulate. And, any implant that delivers electricity to the brain, with our current technology, has a limited lifespan due to the brain’s immune system rejecting the implant (this is the aspect I studied).
Probably not. To get input from the brain, you need to place a sensor near it. But this device doesn’t get inserted into the brain, it sits in the scalp.
There are plenty of non-invasive brain reading technologies though, like EEG and near-infrared spectroscopy. They’re just big and bulky with low resolution.
Edit: in the case of prosthetics, it depends on where the disconnect is. If the brain and spinal cord are intact and the issue is in the periphery, yes, you can read the signal far away from the brain (namely the spinal cord) and then work from there.