But does a neuro have a maximum number of connections?
No, they do not have a maximum. They actually make way too many at the beginning. During fetal development and childhood, neurons in the brain make tens of millions of connections that will eventually be destroyed during synaptic pruning. This occurs from age 4 to puberty, and is a good thing since they're just wasting energy. It also allows the brain to chose which connections are the best.
When a person has a brain injury are the other neurons "picking up the slack" or are they rewiring themselves to preform the task the damaged area did?
It's kind of a combination of the two. Think of it like stopping all traffic on a major highway running through a big city. Taking another highway is not an option, so traffic is diverted to the city streets. The shortest route to the destination, if it exists, will grow and eventually be able to accommodate the new traffic. This is an example of synaptic plasticity and happens all the time, but usually not to the same degree. However, I think it is rare for new connections to be made as we become older.
is our brains ability more closely a function of the number of neuorons and neural connectiosn or they way in which they are wired
The number of neurons and connections are important, but having more than necessary just gives redundancy and these generally do not survive. I think the more important factor is each synapse's ability to change and respond to stimuli. Well that's my theory anyway
Oh btw, I was talking about neural networks. Absolutely, there is redundancy between the two hemispheres of the brain.