What is their relationship with their family/friends?
For Kaito, his family is his mom, his dad's old assistant, and himself.
His dad was murdered during one of his magic shows, and Kaito eventually took up his mantle of KID. He initially honored his memory by continuing to practice magic and spread cheer the same way his dad did, but as KID, he goes a step further by tracking down the killers and trying to kind the jewel his dad died trying to protect. Kaito's mom is usually physically absent from his life because she travels around a lot, but they keep in contact via an in-universe Skype equivalent, and they have a very cozy relationship. She is very much aware of what her son spends his nights doing, and she gives him support in her own way.
Next is Jii!! Jii is the assistant of Kaito's dad, and he's initially a grandfather figure to Kaito. When Kaito becomes Kid, Jii becomes his assistant as well, and they are ride or die. Jii helps Kaito with everything related to heists, and he takes part in them as well when Kaito needs some extra help. The mid-air walk? Jii was in a helicopter helping him along. The teleportation magic? Jii was using sandbags and acting as a human pulley. The man is old, but he does his best. He's not as skilled as Kaito when it comes to imitating voices and other things, but he'll make sure Kaito's heists go as planned and that Kaito makes it home safe every night he goes out. He would lay down his life for Kaito, and Kaito would do the same in a heartbeat.
Aoko is Kaito's best friend, but she's also his waifu, so I don't know if you want to know about that??
What is their established relationship that is not their waifu (say like a close friend that they didn't want to lose or with a parent that they really love)?
Since I'm more knowledgeable about the Detective Conan side of Gosho's work than the Magic Kaito side, I'm gonna go with Kudo Shinichi/Edogawa Conan. Maybe
@Zirconium can tell you more about Kaito's dynamic with Hakuba or Akako, or go more in depth on Jii.
Kaito and Shinichi's relationship is predated by their fathers' relationship. When Kuroba Toichi was Kaitou 1412, Kudo Yusaku was the one who named him KID. They shared riddles and codes with each other in between heists, and they had a very healthy respect for each other. It's technically unknown whether Yusaku knew who Toichi actually was, but as their personal lives did mix with each other, it's likely that Yusaku made the connection when KID disappeared around the time his magician friend died in a tragic accident. If this hadn't happened, it's highly likely that Shinichi and Kaito would have met before a heist pushed them together.
//coughs Anyway! With KID's revival, the rivalry/odd respect was revived as well. Kaito and Shinichi first met in Magic Kaito. KID was stealing the hands off a clock tower (for Aoko, ye olde waifu), and Shinichi gave him a run for his money. The heist ended as a truce of sorts, and Shinichi was able to see that even if KID didn't actually steal the hands, he had accomplished his goal of keeping the clock tower from being torn down (again, relates to Kaito's relationship with ye olde waifu). After this, Kaito crops up in Detective Conan off and on, giving the shrunken Shinichi the light-hearted mental exercises he needs.
In the manga, there's nothing that confirms Kaito knows Shinchi = Conan, but in the anime, he definitely does. He pointedly saves Shinichi's ass from suspicion by disguising as him in a movie, and he also uses Shinichi as a disguise for his own benefit too many times to count, knowing that Shinichi is the one disguise he can wear that won't be revealed easily. As for Shinichi knowing who Kaito is, nothing has been confirmed in either the manga or anime, but Shinichi is one of the few people who knows that KID is actually a teenager (and therefore, not the original KID) who looks eerily similar to him. He also knows that the previous KID had a relationship had a relationship with his father. Due to recent manga spoilers, I'm of the belief that Shinichi knows, or is incredibly close to figuring out, who Kaito is, and it hasn't been revealed out of respect. For the first time in the manga, they worked together in a way that is usually only seen in anime or fanfiction, and to me, that speaks to how much they trust each other.
Kaito doesn't treat "Conan" like a child, and Shinichi is not above working with a criminal. They banter and keep each other on their toes, and whether or not KID gets away with the jewel of the the week, they both come out of it pretty satisfied. They're friends, which they really shouldn't be. Despite what their goals may be, they're on the opposite side of the law. Shinichi is a stickler for truth and justice, and Kaito's opinion on detectives really isn't all that great (read: Hakubastard). However, Kaito is an exception for Shinichi, and Shinichi is Kaito's favorite critic. It's very likely that KID will take part in the eventual takedown of the organization Shinichi is after, and if the #SameOrg theory doesn't pan out, I expect Shinichi to appear in Magic Kaito as an ally against Kaito's org. Kaito quite literally risked his life to help Shinichi in a spoiler-tastic event, and I fully expect Shinichi to return the favor.
Their relationship isn't common by any stretch of the imagination, but over the 20+ years of their respective storylines, it's grown into a relationship in which a thief and a detective trust each other in ways that very few people do.