1. Why do Bitcoin Cash users find Bcash derogatory?
When they decided to go through with the fork, their aim was to be a differing version of Bitcoin, so they wanted to keep the association between that chain and the earlier one. They believe that Bcash removes the association between Bitcoin Cash and Bitcoin, and because it originated mainly from r/bitcoin where most people are opposed to Bitcoin Cash, many of them believe that this was deliberate.
2. What is the difference between Bitcoin Unlimited and Bitcoin Cash?
Bitcoin Unlimited proposed introducing the ability for miners to change the block size using a new system called Emergent Consensus. IIRC Bitcoin Cash just did a simpler block size increase to 8MB.
Also, Bitcoin Unlimited required support from 75% or more of miners for them to activate it, whereas Bitcoin Cash's intention is to allow the market to choose between the two chains over time instead of gathering support beforehand.
However, because they both share the belief that Bitcoin should be scaled with significant block size increases, the same people tend to support both proposals (and Bitcoin Unlimited supporters tend to support the new Bitcoin Cash chain).
3. From what I understand Bitcoin Core is a full node wallet? Is that to help broadcast transactions to other nodes? Is there something special about it I am missing..?
The most important benefit of a full node is that you can personally verify that none of the network's consensus rules have been broken without relying on other full nodes to verify this for you. It's how you run a trustless wallet.
There are also
other benefits to running full nodes.
4. I am learning python in order to learn to interact with the bitcoin blockchain so that I can learn more about how the parts fit together, any advice on what to build first?
Someone else will have to answer this.