These are the relationships Alan has with the other characters in the show.
Darwin and Alan usually interact through Gumball (that is, when Gumball with Darwin at his side has dealings with Alan). When Gumball tries to make Darwin jealous by hanging out with Alan, Darwin does not mind at all and even says that it is great. Alan then convinces Gumball to go to Darwin to save their friendship. In "The Photo" Darwin and Gumball suspect Alan, and he accidentally pops him. Alan "turns his other cheek" instead of getting mad after Darwin admits that he popped him intentionally. Darwin later helps Alan and Carmen get back together in "The Storm." In "The Saint," Darwin finds Alan's constant kindness to be almost sickening, but still disagrees with Gumball's behaviour towards him. In "The Faith," Darwin tries to help Alan cheer up out of obligation due to it being the only way to return the world's color. However, he does genuinely seem to want Alan to be happy, and tries to get Gumball to be kind to him, despite it being almost impossible.
Alan and Carmen both love each other very much. Their relationship is so perfect, that other people, filled with envy, want them to fail. The only problem their relationship has is the fact that Alan is a balloon and Carmen is a cactus— balloons are prone to popping upon contact with spines, and cacti are prone to being covered with spines. Alan has already popped four times because of this unfortunate combination: once in the early reel, again in the trailer for the show, a third time in "The Banana," and a fourth time in "The Joy." Despite this, he is still devoted to Carmen.
Their relationship has also been called "cheesy" by some, namely Masami and Gumball. Their comments about their love for each other are filled with sappiness, like "if Alan was a cheeseball, I'd want seconds." The relationship between the two is mutual, and has already been the target of plans to break them, as in "The Storm" and "The Saint," since the couple is classified as "perfect" as well, which causes jealousy and envy in other students, but they always end up reconciling in the end.
In "The Faith," the memory of being with Carmen is one of the key things that cheers Alan up— the memory is even described as "a memory of perfect bliss."
Alan and Gumball are shown to be on relatively good terms. Though Gumball often takes advantage of him, Alan, being the nice guy he is, does not seem to mind. He helps Gumball in whatever way he can, usually by providing advice, like in "The Third," where he inspired Gumball to chase after his best friend, and in "The Photo," where he advised Gumball to just be himself. In "The Storm," Gumball ruins his relationship with Carmen, but also helps bring them back together. At the climax of the episode, he finally gets annoyed with Gumball's constant screw ups and yells with such ferocity that Gumball shuts up out of fear. In "The Saint," Alan takes the blame for Gumball's damage out of pure kindness. Gumball, angry at how nice he is, purposely makes Alan's life a misery to find his breaking point, but later on apologies for his behaviour, yet still finds Alan's kindness to be an annoyance.
In “The Faith,” Gumball and Darwin find Alan and realize that he is the reason Elmore is in greyscale. Alan explains that because he lost faith in everything in Elmore, and also because Gumball had always been so unkind to him, Alan had given up on the world, and thus the world started to fall apart, as Alan's extreme faith in the world was what kept it together: when things went wrong, Alan would make them right by doing odd jobs and helping out in general. Gumball now has to get over his hatred of Alan while he and Darwin sing a song about having faith in the world, which cheers Alan up, restoring his color and the world's. From this point on, Gumball and Alan seem to be friendlier.
However, they argue constantly in "The Decisions" due to Alan's logical advice clashing with Gumball's excitement-driven advice. At one point, Alan even shouts in annoyance at Gumball, which he is not wont to do. They do appear to have made up at the end, as they go for ice cream with Darwin and make pleasant conversation.
Masami has had an unrequited crush on Alan ever since she laid eyes on him. Unfortunately, Alan does not return this feeling. The only reason he went out with her in "The Storm" was to convince Carmen to get out of her depression and date other people. After hearing his cheesy love story of Carmen, however, Masami gets disgusted and storms out of the room.