Why do miners have to be evenly split to start with?
I doubt it would work with a great certainty if you were to disconnect two portions of miners and both of them have the same hashrate. Bitcoin Core will only accept the chain with the longest valid blocks and you need to ensure that you are spending to the merchant on the correct chain.
Also, they use "communications delay" but for bitcoin, this would be more of a disruption between the 2 groups right?
If the two groups do not know the blocks that each other is mining, one of the chain will eventually be orphaned.
For example, if group A mines Block 1, Group B would, in a perfect scenario mine Block 2. However, since they do not know the block has already been mined, they will mine their own Block 1 and thus have a competing blockchain against Group A. If Group A were to have a higher hashrate, there is a higher chance of the chain being accepted by the network.
Also the need to isolate the node you are purchasing goods from to one side.
Yes. You need to know which fork the merchant is on. See this example:
https://bitcointalk.org/index.php?topic=152348.0.