Derby:
 Centers Trade & Spread as Ends Run;
 The traffic pattern has the Ends moving around the Centers.
3 By 3:
1) Identify each group of 3. Everyone in the group must be facing the same direction,
and they are generally in a Tandem of 3, a Couple of 3, or within a Disconnected (Once Removed) setup.

2) Visualize removing the center dancer from each group of 3, doing
the call, then putting each center dancer 
back between the 2 dancers that they were initially between.
Dance-wise, the center dancer (a.k.a., the "cheese")
must stay between the other 2 dancers in their group of 3 throughout
the entire call.
Single File:
*** Either the notes, or your interpretation is wrong. The person in front does the part of the dancer who 
*** would normally first reach the dividing line between the couples or mini-waves within the normal version 
*** of the call. Hence on a Single File Flutter Wheel, the center acts as a Belle, whereas in a Single File 
*** Reverse Flutter Wheel, the center acts as a Beau. Since on a Beau Hop, the Beau reaches the center 
*** line first, on a Single File Beau Hop, the centers act as Beaus.
Diamond Concept
I don't really like your definition here. It is hard to understand if you don't know the Concept. It starts with "movements on the outside". What does outside mean?
Some explanations you will find in the comments. I would suggest that you reword this definition a little 
Lars Erik
Diamond Concept
Why is it not allowed to use this concept with p-p Diamonds? 
Lars Erik
The second picture on Trixie Spin: 
as is not translated. It should be : medan
Connect the Diamond:
Make note that original points can roll.
Just as in Scoot & Weave, there are 2 different kinds of Turn & Weave.

1) From a Single Starting DPT (i.e., Zero Tag) or a Single ¼ Tag: Centers Arm Turn ½ and Step Thru, then (passing shoulder as the arm turn) Weave. (similar to Centers Arm Turn ½, all Extend, Any Hand ¼ Thru)

2) From a Single Eight Chain Thru or a Mini-Wave Box : Arm Turn ¾ then Weave. (similar to all Arm Turn ½, Any Hand ¼ Thru)
Short Cut was written by Joe Uebelacker, according to Joe.
Grand Working:
*** GRAND WORKING requires a 4-dancer call. The outside 4 always work Split.
*** Centers work with the group of 4 determined by the direction 
(In, Out, Right, Left, Forward, Backward, Clockwise, Counter Clockwise) 
or the position (End, Center, Beau, Belle, etc.)