I can answer most of this for the Shuttle.
Is there a legend for all of the symbols? Is there a formal grammar?
Yes. The document that controls the preparation of the Flight Data File (the formal name for the collection of crew procedures) was Annex C of the Space Shuttle Crew Procedures Management Plan: Space Shuttle Flight Data File Standards and Specifications
Every symbol and its use is explicitly spelled out in this document. Here's an example for one similar to one you mentioned.
I am sure NASA spent an in inordinate amount of time developing these
lists, are there any guidelines and a rationale for their development?
Also yes, the same document. Chapter 3 of the Shuttle Crew Operations Manual is all about FDF and explains in some detail the processes for maintaining and updating it.
For example, the form to be filled out to change a procedure was JSC Form 482. Here is the flowchart for processing those forms.
How are these lists used? Is one person reading them and a second one
executing the commands?
For ascent and entry, the time-critical procedures were affixed to the wall adjacent to the commander and pilot in what were called the "flip books". The mission specialists in the back had bound copies.
(Photo credit: NASA, annotation mine)
The front-seaters would (theoretically) read the procedures from the flipbooks and perform the switch throws. The back-seaters would follow along and check that the proper procedure was executed and the proper switches flipped.
On orbit, bound copies were used. Having a backup crewmember to help was encouraged for all procedures and strongly encouraged for critical procedures.
is there any software that checks the syntax and makes sure the references are ok?
For Shuttle standard office word processing software was used.
For 5, I know little about Russian procedures, hopefully someone else can answer.
A good collection of shuttle-era FDF can be found at the JSC FDF Page which includes examples of the flip books, bound documents, and both nominal and off-nominal procedures.
Just learning what FDF to use when was a major step! Here's a handy guide, also from the SCOM. The top bar (white background) lists the controlling documents for nominal activities. The gray bars show the malfunction books appropriate for the stated mission phase.