the Mario Bros' mom (who I call Luana in my story) couldn't take the idea of her kids being placed in danger any longer (considering that they were kidnapped like three times before at this point), so she demanded the family move out of the Mushroom Kingdom. Mario and Luigi spend the remainder of their childhood and teenage years in Diamond City; Luana suggested they move there because it was mostly inhabited by humans (as she feels the bros. could relate better with their own kind) and had next to no monsters.
Kamek and Kammy Koopa are siblings, Kamek being the older brother while Kammy is the little sister (their ages aren't too far apart though).
Having been around them quite often as a baby, Mario can somewhat understand the language of the Yoshies, but he can't speak it. Yoshi (the main green one) will usually act as his translator when Mario talks to other Yoshies that can't speak human English, being bilingual.