What is a "wasteful" execution? And a "schedule"?
I'm not completely sure of my answer since I don't have the book but I think that:

By "wasteful" execution they mean an execution that follow $A$ but with a lot of messages. There are trying to prove that for $n$ processes you may need $\Omega(n\log(n))$ messages. So they consider a ring with $n/2$ processes and the worst execution and they want to combine two of this rings and of those executions to prove that for $n$ processes you will need a least $n\log(n)$ messages.  

By scheduler I think the mean a function $\sigma$ that a each state of your system associate a process and an action to be performed. A fixed system and a scheduler are equivalent to an execution (since you can see it as $s\xrightarrow{\sigma(s)}s_1\xrightarrow{\sigma(s_1)}s_2\xrightarrow{\sigma(s_2)}\dots$ But schedulers are often more easy to work with since they are functions so in the proof you don't need to manipulate indexes of where you are in the execution.

I hope it helps, please ask if I missed something.