They are clearly fans of Little Witch Academia, hahaha. Three characters in that shot look very clearly inspired by LWA characters dating back to the Enchanted Parade. Not to mention the character of the setting.
They're a developer (Starbound and the upcoming Wargroove) who I believe were able to leverage their money / popularity from Starbound to start publishing for other indies like Stardew Valley and Risk of Rain. I'm pretty sure this game is completely in-house though.
This is correct. They're developing Wargroove in-house. All of the other games listed on their site, they're only acting as publisher (though in some cases like SDV, they're also lending developer support, helping Concerned Ape implement multiplayer since it's quite complicated).