What are the characteristics and themes present in Gundam characters based on Char Aznable? Across all Gundam universes, there is always at least one character based on Char Aznable from the original Gundam series. (I say "at least one" because sometimes there is a softer character that is less obviously based on Char.)


In Gundam Wing, the obvious Char knockoff would be Zechs Marquise; the tell-tale characteristic is the mask. He was the sister of Releena and the child of the Peacecraft family. This an obvious nod to the fact that Char was really Casval Rem Deikun, son of Zeon Dum Deikun. His sister was Artesia Rem Deikun, who took the alias Sayla and was an active member aboard White Base.
Quatra is the less obvious Char clone, who shares Char's blonde hair and is named after the number 4. (Char in multiple Indian languages means four and his alias in Zeta Gundam was Lt. Quatro.)
In the most recent Gundam Unicorn, Full Frontal is obviously the main Char character (many in the show itself believing him to be the famed Red Comet) while Ensign Ridhe is the softer Char character (indicated by his blonde hair, his family's ancestry, and rivalry with the main character).


The Char character usually has some kind of "cool" nickname; Char's is Red Comet, and Zechs has the name Lightning Count. Additionally, their mobile suit is usually colored red or white. Would this make Athuran Zala also a Char character, with his signature Red mobile suits?

Basically, what I'm wondering is: Is there a defined set of characteristics like the above mentions and their occurrences across all Gundam series (whether they be Universal Century or not)?
It seems that there is always a masked antagonist in the Gundam series, but they vary in how much they resemble the original Char.

In Gundam Seed, it is Rau Le Creuset . Masked, and related by blood to a member of the protagonists camp. IIRC he is also a noble who stands to inherit, but unlike Char Aznable, 


   his family is not usurped.


In G-Gundam, it would be Schwarz Bruder. It is a bit tricky to bring him in the equation, though, because G-Gundam is much simpler than the other Gundam series.

Going by these examples and the ones mentioned in the question, the constant features seem to be


The character wears a mask to hide his true identity.
The character fights for the (apparent) enemy.
The character is male.
The character is related by blood or cloning to the protagonist or a close ally.


The features that vary among the Char Aznable knockoffs are


The character has a strong sense of honour and fair-play (IIRC Rau Le Creuset is the exception here).
The character is a noble.
The character bears a secret grudge (Schwarz Bruder would be the exception).
The character has a nickname (again Schwarz Bruder is the exception).


With respect to Quatre in Gundam Wing, I don't think he is a Char-based character. Quatre makes no secret of his identity and doesn't wear a mask. His name is not a clue IMO; almost all characters in the show were named after numbers in French. The role of Char is aptly fulfilled by Zechs Marquise.