Juan was the leader of the Sootopolis City Gym before Wallace was. Juan was actually Wallace's mentor, and taught him everything he knew about Pokemon, and Battles. Wallace and Juan share a love for water-type Pokemon, as they both use them as Gym Leaders. Juan eventually retired after teaching Wallace, and passed down the title of Gym Leader to him. In Pokemon Emerald, Juan takes up the mantle of Gym Leader once again when Wallace becomes the League Champion.
It isn't explicitly stated, but implied that Juan also taught Wallace about Pokemon Contests. This is in the games, however, and Wallace is not as active in Pokemon Contests in the games, as he is in the anime and manga. In the anime, Juan is known to put on shows and displays with his Pokemon, so it is likely that he was the one who taught the very Contest-active anime-Wallace how to compete with his Pokemon. Wallace in the anime has an incredible passion for contests, and it seems likely to me that Juan was the one who instilled this love for contests into a young Wallace.
Both Wallace and Juan are considered to be fashionable individuals, and have a bit of a female fanbase in Sootopolis City. Wallace and Juan must have a very close relationship, considering their mentor/student status. It was Wallace's goal to eventually take over the Sootopolis City Gym, and Juan basically groomed him for the position. It is implied that while retired, Juan still lived in Sootopolis City. So, Wallace and Juan likely still see each other quite a bit. I imagine that Juan is probably very proud of Wallace, especially since he was able to eventually gain the title of Champion. A fun fact about Juan is that in the anime, Juan uses the same Pokemon Team that Wallace uses in Ruby/Sapphire.
While Winona and Wallace have no interaction in the games or anime, they have a very close relationship in the Pokemon Adventures manga series. In fact, the two were involved romantically, before they eventually separated before the start of the Ruby/Sapphire series. Winona was eventually the one to break off the relationship, stating that she was uncomfortable being a relationship with someone 'stronger' than her (likely a reference to her Gym being the 6th, while Wallace holds the 8th). Winona basically felt smothered in their relationship, thinking that she couldn't measure up despite everything she did.
Wallace obviously cared for Winona a great deal. After winning the title of Champion, he declined it not just to return to being a Gym Leader, but also so that he could remain close to Winona, who had just become a Gym Leader at the time. I don't have any question in my mind that Wallace still cares for Winona, and that he was very happy with their relationship. Despite their separation, they remain on good terms with each other, and Wallace still very much cares for her. While they are on good terms and fairly friendly with each other, Winona is obviously still a bit insecure around him, and takes his suggestions as him questioning her leadership abilities. She is at this time, very quick to remind Wallace that they no longer share a relationship. While she is a bit harsh about it, I honestly think that this stems a bit from her insecurity, and her unhappiness about that.
She isn't completely cold towards Wallace, obviously. I think her insecurities just get the better of her on occasion. But, this doesn't stop her from being a competent leader, as well as Pokemon Trainer. She is able to move past this in times of crisis, and work together with Wallace to protect Hoenn from the threat of Kyogre and Groudon. The two of them are seen again in the Emerald chapters, when they both attend the wedding of Riley and Wanda. Sapphire pokes fun at Winona, asking if she had developed feelings for Wallace again after the ordeal they had been through. Winona blushes, and tells Sapphire to stop making fun, although she does not deny it.
Steven Stone and Wallace are close friends not just in the games, but also in the Pokemon Adventures anime. It is unknown if they are friends in the anime, but they may be considering Steven would have had to have gotten the Champion title from Wallace. Before the start of the manga, Wallace actually won the Champion title from Steven, but declined the position so that he could return as Gym Leader of Sootopolis City. The two of them are close friends in the manga, with Steven coming to find Wallace when he [Steven] needs assistance with something. Furthermore, they are close enough that Steven was able to guess Wallace's reasons for declining the Champion position.
When conflict arises in the series as the result of Ground and Kyogre battling, Steven eventually convinces Wallace to take back the Champion Cloak. Steven and Wallace go together to awaken Registeel, and use it to help protect Sootopolis City from the backlash of the Kyogre/Groudon battle. The strain of Registeel is too much for Steven though, and he passes away shortly after. Wallace is greatly upset by this, but vows to take up the Champion Cloak and continue fighting.
This relationship extends to the games as well, with Wallace having dialogue mentioning Steven on more than one occasion. The two are seen to together multiple times as well. Wallace compliments Steven's skills as a trainer, and seems to know quite a bit about Steven's love for rare stones and his hobbies. It is also noted in the Delta Episode that Wallace and Steven talk pretty frequently with one another. When Steven opts to travel the world, he then asks Wallace to take over the role as Champion (which is a reference to their roles in Emerald).
Expect this section to be updated a bit once I finish up Alpha Sapphire.
Ruby and Wallace have a pretty close relationship in the Pokemon Adventures manga series. Ruby is a fan of all things beautiful, and strives to do well in Pokemon Contests. By chance, he attends a contest that Wallace was participating in, and he was thoroughly blow away by Wallace's skill as a competitor. Ruby then begs and begs Wallace to take him on as an apprentice. Initially Wallace declines, but eventually agrees after discovering Ruby is the son of a Gym Leader, and witnessing his love for his Pokemon. Ruby is thrilled, and the mentor relationship begins.
Things are initially sound with their relationship. Ruby is eager to learn, and takes Wallace's advice to heart. Though, Ruby is still young and very emotional. He rushes off to Slateport city to compete in a contest. When he begins to lose, he angrily blames his Mimi (a Feebas), and yells at her while blaming her for losing. Wallace however, is present and is furious with what he has seen. He gives Ruby one hell of a talking to, and lays out all of the mistakes and selfishness that he [Ruby] has displayed. Though shocked, Ruby is eventually able to realize his mistakes because of this. While Wallace can be harsh, he acts with Ruby's interests in mind. Ruby is able to grow as an individual because of this.
Ruby is eventually able to become a contest master, under the tutelage of Wallace. Though there may not be much left for Wallace to teach him, the two still are seen spending time together, and are good friends. They are seen together at social events such as the wedding of Riley and Wanda in the Emerald chapters. I imagine that Wallace (much like Juan) is quite proud of how his apprentice has grown. Wallace is last seen helping out Ruby and Sapphire, and helping with the destruction of the Grand Meteor Delta that threatened Hoenn.
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