Character Analysis
Ugh. Big mouthed, chauvenistic, domineering, arrogant. These are all words that easily understate the creature that is Riot. He is fiercely superficial in his outlook - this is illustrated in no better way than his obsession with Jem, which is based on looks alone ("I am the perfect man, you are the perfect woman, we belong together" - Stingers Hit Town). The fact he has no interest in where Jem is from or who she really is firmly indicates his preoccupation with himself and his own interests, and that his interest in her is merely her look, not her personality. Equally his cruel treatment of Pizzazz is based entirely on feeding his own interests - he keeps her hanging on in order to gain control of the Music company and to forward himself and his band into the music business. Charismatic when on stage, he has a certain rapport with the audience that helps to forward his image as something of a heartbreaker. He has the ability to capture the attention of the crowd, and is a born performer in a total different way that both Aja and Pizzazz are, in that he uses his voice and his appearance to his advantage, rather than focusing on the music itself.
This isn't to say that Riot doesn't have a strong love of music. In Riot's Hope you get an eye opener into the boy's childhood and it becomes apparent that maybe Riot's attitude to the world as an adult is largely based on his insecurities growing up. He has a lack of support from his military minded father, particularly when he got a dishonourable discharge from the armed forces,and in that vein must have felt himself a failure in his father's eyes. Despite this he had the determination to fight back and do what he really loved for a career - but in many ways he seems to be trying to 'prove himself' at every turn. His dominance over the Stingers, his dislike of change (Minx's defection causes him a great deal of stress) and his adoption of the royal outfits in Straight From The Heart suggests his desire to be on top of things once and for all (and prove he isn't a failure).
Despite his chauvenistic attitude towards the women around him (Jem, Jerrica, Pizzazz), he has a great fondness for his mother and even makes up his rows with his father in order to save her life. I sometimes wonder if Mr Llewelyn is worried about his son's sexual orientation (and on occasion have admittedly wondered about it myself). Mr Llewelyn's motivation is that his son has no ambition for the army, wants to grow his hair long and would rather play piano and guitar than indulge in what he sees as more manly activities. My own personal speculation about Riot's sexuality is based more on his conscious desire to be adored by and to control women, as if he's not entirely secure around them, and his attraction to them is never deeper than superficial. The only time he goes deeper with Jem is when his mother is sick and he needs a friend...he does not develop on this established bond in any romantic sense, despite his pursuit of her in other episodes. It seems more to me sometimes that he's more conscious of his image and what people expect of him than what he really wants to be. I'm not sure Riot is gay...but I'm not certain either that he is entirely heterosexual and any deviant leanings within him have been so firmly suppressed that he's confused about how to deal with women. It also seems rather strange to me that someone who plays things as such a casanova of a character spends all his time living with and playing with two women, but never indulges in any romantic relations with them. It seems a little out of character for him not to use his charisma to break them down, especially since in the flashbacks it seems that Minx maybe has something of a crush on him. But this is wild speculation, and nothing more...as I am no great fan of applying firm sexual deviances to characters which, in an eighties cartoon for kids were never actually given them.
His arrogant, cold nature is broken down once or twice, such as in A Father Should Be when he helps Jem find BaNee's father, since Jem helped bring him back together with his. I'm not sure that everything in Riot is bad, but a lot of it is misaligned and misplaced. His superficial attitude to the world is perhaps a way for him to avoid the deeper issues of his upbringing and the discouragement from his father towards his musical aspirations. He also wants things entirely his own way, since he would rather quit the band Nirvana than bow to someone else's wishes. (Riot's Hope)
Also, his treatment of women would seem to be little more than a reflection of his father's treatment of his mother, since Mr Llewelyn is decidedly domineering towards his wife on more than one occasion, both in flashbacks and when Riot returns home to tell his parents of his success. Therefore perhaps not all of Riot's unpleasantness is down to him.

Friendships/Roles
Riot adopts several roles throughout the series. Firstly he plays the role of big brother where his bandmates are concerned. Rapture and Minx both look to him for leadership and to get them out of various problems (such as in Midsummer Nights Madness when they are being pursued by angry Greeks). He also plays the role of the romantic hero - flirting with Jem and trying to manipulate things with Jem in his favour (midsummer nights madness, Day the Music Died). But in truth it must be said that Riot's closest relationship is with himself and his own ego. There is noone who ranks quite so high in his estimation.
Another of his roles in the series, however, is the role of prodigal son (as has been discussed above) and a fragile bond exists between him and his parents which is always under strain from his desire for independance.