In answer to your questions
Heretic,
I am enjoying our discussion! FYI this "new idea" about singletons is actually from Richard Idemon in his book "The Magic Thread" (now out of print, but available for about $40 and up). In the book, Richard takes the quadruplicities of the houses (Fire, Earth, Air, and Water) and groups them as "personal" (signs/houses 1-4) "social" (signs/houses 5-8) and "universal" (9-12). He then looks to see how many signs a person has in each of the three sections AND how many planets a person has in each of the three sections. The book is well worth picking up, as is his other book "Through the Looking Glass".
On my website I group the Cardinal, Succedent, Cadent similarly into three groupings: Beginnings (houses 1-3) , Development (houses 4-6), Achievement (houses 7-9), and Maturity (houses 10-12). The same sort of grouping could be done for the signs.
Again, to keep things simple, I group signs/houses by Fire, Earth, Air, and Water and Cardinal, Succedent, Cadent. While I analyze planetary energy focused in a house (planets in a house) in terms of Beginnings, Development, Achievement, and Maturity and most recently (thanks to Richard) Personal, Social, Universal. By the way, I actually do NOT use these sign/house terms but instead prefer Stephen Arroyo's Identity, Material, Social, and Emotional, and Action, Security, and Learning. I like to use these words because it means I do not have to keep "translating" the more commonly used astrological terms into something I can make sense of!
You are an authority on you! If you are able to "pull in" the grand trine energy, that is fine, but remember that the grand trine aspect can tend to ISOLATE a person in an "everything is fine" world (for more on this see Noel Tyl's works).
A grand cross IS a grand square (simply different terms for the same aspect pattern (and you definitely DO have a grand square/cross in your chart, not a T-square). Rather than create a complex pattern of interlocking grand squares in a chart, I group stelliums in a chart as "energy focuses" and look at how they relate AS A WHOLE to the rest of the chart. So I look at ONE grand square of Moon, South node, Pluto-Mars-Saturn, Sun OR Mercury-North node. This forms one grand square with two options: either tieing in the Sun into the grand square or tieing in the Mercury-North node conjunction. For simplicity of interpretation (since the two options create quite a different effect) I call it TWO grand squares. In my opinion the most important grand square is the one that links your North and South node.
Again, for simplicity, I refer to aspect patterns (grand cross/square, trine, yod, etc.) as FOCUSES of energy (following the lead of Stephen Arroyo). These aspect patterns act to channel energy into a particular part of the chart: Squares focus on the corners, trines focus on the three points, yod focuses on the intersection of two quincunxes, etc.). So the more "focuses" a person has in the chart the more their energy is DIRECTED towards a purpose (instead of simply being scattered around their chart). Your chart energy is VERY focused in this way, indicating you have definite purposes and agendas in life.
The "mystic rectangle" is simply a name for an aspect pattern in which four planets/points are in alternating trine/sextile position to each other and which all oppose the opposite planets/points (for a total of two oppositions). It has the same "four corners channeling effect" as the grand cross/square, only it has less stress involved (due to the trines and sextiles).
You have Sun (performing arts) square (energy needs to be combined with Saturn (career) conjunct Mars (action) conjunct Pluto (power) focused in the 5th house (performing arts): I think you can accomplish anything musical you want to accomplish. Neptune (music) is tied in on your descendant and is a strong focus due to the mystic rectangle channeling your energy. You may not write music that lasts hundreds of years, but it should at least last for a couple of decades!
Helping,
Tim