I don't consider Impa to be a minor character per se. In fact she does many actions that make the story move so she is not exactly minor, considering how relevant she is.
My favourite characters besides the main ones, would be Skipper, Fledge, Pipit, Gully, Beatrice and Beatrux. I like pretty much all, but these stand out. I have a soft spot for Skipper. Not only he helps you a lot but unlike the other robots he knows that he lives in borrowed time. His story is quite sad though. If you read the wallposts in his house you notice that he has children, is an amazing captain to his crew and that he and his family have had an amazing time together. The thing is, he wants desperately to see his family back, but we never no. if he actually does. Although you do defeat Scervo, probably allowing him to return home this is no fully confirmed. Actually is kind of melancholic. But in general I really liked his story and character.
Fledge on the other hand is quite cute. I like how he actually admires Link and how he wants to be better and brave like Link is. Also, I feel sorry if how he is constantly bullied, and I kind of sympathized with him. And he does help you too! He gives you the Pouches for free. Unlike the othe guy who sells it more expensive each time you buy him! I like his name aswell.
I didn' like Beatrice much, but its very hard to not like her after she really begins to have feelings for you. And Beatrux is also kinda of cool. I actually cared more to finish his sidequest just to see him become a human. I did like his rewards, but I personally did care enough for him.
Pipit is also kinda cool. He has his temper, especially with his mom, but he does care for you and gives you some advice from time to time. His sidequest was also a good one.