Not much is known about Zelda's family; they are rarely mentioned or seen in-game. The king and the prince who were related to Zelda in The Adventure of Link are never even named—their actions merely provide an explanation for Zelda and the Triforce's conditions. It does seem though, that the King deeply trusted his daughter, as hinted in the prologue. It is also stated that Zelda's brother, despite his actions, did care for his sister and was devastated when he realized what his actions caused to her. The next time any known interaction between Zelda and a member of her family is mentioned is in Ocarina of Time; where the King of Hyrule (who is also Zelda's father) appears as an unseen character. The only thing that is even hinted about their relationship in that game though, is that the King did not seem to take all of his daughter's words seriously, which caused his downfall in the Adult Timeline and Fallen Hero Timeline.
I feel like they focused too much on making the game new and exciting rather than balanced and fun but they still did pretty good at throwing everything together. It has tons of tracks, vehicles, characters, and is probably the most re-playable version of the series because there is so much stuff to unlock. I unlocked everything in the game using a stock character and vehicle so the unlocked stuff isn't overpowering like in past games. The unlock-able characters and carts seem well placed and often help you with your playing style. For example you unlock the fast characters while trying to do time trials or you get the agile carts from gold on the harder tracks.
When Zelda's power failed to awaken on Mount Lanayru, Urbosa told Zelda not to give up hope as she did all she could and noted Mount Lanayru wasn't her last shot as anything could spark her powers to awaken. When Ganon appeared Urbosa initially wanted to take Zelda to safety but Zelda refused wanting to fight alongside her comrades even without her powers which Urbosa did not object to, understanding and respecting Zelda's desire to stand alongside them against Ganon along with her courage and sense of duty. Ultimately Urbosa was correct about Zelda's powers as the spark she spoke of occurred when Zelda selflessly tried to shield the exhausted Link from an attacking Guardian saving Zelda and Link. Even In death, Urbosa continued to support Link and Zelda as a spirit once freed from Thunderblight Ganon's imprisonment.