I'm doing this at about 11:30pm my time and I'm about to go to bed so I'm really tired while writing it. If I make mistakes then please point then out and I'll edit them as soon as I see your message. :)
Here goes!
Richard's relationship with Mia is rocky, to put it very, VERY nicely. Her personality is a near polar opposite of his own, and they have clashed many a time in the past. The primary reason for this is because when Richard was still in the process of discovering himself and locking in his disciplined and intellectual side, she managed to convince him to do something he shouldn't have. She convinced him to cause a minor disturbance in the streets of Vilkaf which got him in trouble with the Vilkaf police while she managed to slip by and do whatever it was that she wanted to do. Thanks to Leo Ryan's intervention, Richard was spared serious consequences but never the less kept on the watch list by the police for the next few years.
Richard never forgave her for that.
While he doesn't hate her in any way, he does hate the way she flaunts her looks and takes advantage of other people through them. He also hates her methodology when on a job, and her lacking of respect for authority beyond a few key figures is also a cause of tension between the two. Richard has admitted to himself and others that if Mia just respected authority, he'd at least be able to be in the same room with her and not roll his eyes every time she opened her mouth to speak.
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Because Leo Ryan is a veteran of lightning, he is the one person Richard actually opened up to completely and views him almost as a second father.
It was from Leo that Richard learned to be analytical, calculating, and cautious. Richard also learned his patience when facing down Mia from Leo as well, even though Richard's patience regarding the young woman is much thinner and more easily tested. Leo's tales of dealing with politician's and such proved to be good experience for Richard, as he listened to everything and picked it up very quickly. He has a level head and an open mind, and Leo's experiences and knowledge were a blessing to Richard given the fact that lightning is a wild and incredibly difficult element to both work with and control.
Richard has said more than once that if Leo hadn't been his master in the art of lightning that he'd probably be dead already.
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Richard's relationship with Nathaniel is one of brotherhood in which the two share a distinctly serious attitude towards what they are and how they operate as Warriors. Whenever in private, Nathaniel's more open and hyperactive personality can sometimes push Richard's buttons, but otherwise he's very tolerable and easy for Richard to open up to and speak with. Richard has almost never had a problem talking with Nathaniel about anything that's been bothering him, as Nathaniel proved a good listener and the two of them continue to get along very well to this day.
The only source of tension between the two has been Mia Ryan, as she is the one person Richard truly cannot stand in the group, and the person Nathaniel seems to gravitate towards the most.
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Richard has never quite known what to make of Cha Jung Soo.
While the two of them are not exactly what you'd call friends, they do share something of an understanding. Both are keen to take to private environments with plenty of quiet where they can read, meditate, sleep, etc,. They have not conversed very much, despite their time together, mostly due to Leo's introverted personality and unwillingness to speak most of the time. Still, the two of them know how to work together and do so seemingly well despite the opposing natures of their elements.
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Richard, as with his relationship with Mia, is rather averted to Stella due to her overtly sexual nature.
He doesn't dislike her, but she sometimes just rubs him the wrong way. Her method is slightly different than Mia's but because the two are so similar in the respect that they both flaunt their looks and use overtly sexual methods to get their way, Richard tends to give them their distance for fear of risking an argument and a headache. Stella's personality is different enough that Richard can actually stand her, however, and he has relied on her skills in battle numerous times to earn her his respect.