1. Why is "After Takeoff /Climb" checklist written that way?
Because it's a checklist for After Take off, and during Climb
Does Airbus intend us to say "After Takeoff Climb Checklist"?
Yes
2. Parking Brake As Required
Does Airbus want us to say "Set" or "On" if the Parking brake is indeed on.
Airbus callouts use 'Set' and 'Released'.
3. Baro Ref Challenge
One of my instructors insisted we respond with, for example, "QNH 1011 Set".
Note the "QNH" addition, but I can't find anywhere in the FCOM or FCTM where it states we're supposed to say "QNH", although it is a good idea.
I believe there is an option for setting QFE as well using the Baro knob; that may be the reason this is emphasized upon.
4. Does anyone know of a book that uses the latest Airbus procedures that explains everything in a neat, organized, coherent way?
The FCOM itself 
Sometimes I think I should give up being a pilot and instead make my money writing an Airbus manual that's more... how can I put it.... pilot friendly.