King Rhoam initially supported Zelda's research efforts though as signs of Ganon's return increased eventually he came to believe Zelda was using her studies as an escape and was neglecting her duty as Princess of Hyrule to play scholar unaware Zelda had been training as hard as she could and was using her studies to contribute without her powers. However King Rhoam put his duty before Zelda and scolded her during a Guardian test trying to convince her that she should be focusing every waking moment to awakening her power. Zelda however insisted she already was and tried to explain herself though King Rhoam refused to hear anymore excuses and forbid her from further research. Rhoam attempted to encourage Zelda by telling her that the gossip mongers had been whispering she would inherit a Kingdom of nothing and that it was her destiny to prove them wrong. This however had the opposite effect and led to her having a sense of self loathing due to her "uselessness in the battle field" and inability to awaken her innate powers. She continued to do research such as a survey of the Shrines alongside her Sheikah court poet in secret.
The Legend of Zelda was principally inspired by Shigeru Miyamoto's "explorations" as a young boy in the hillsides, forests, and caves surrounding his childhood home in Sonobe, Japan where he ventured into forests with secluded lakes, caves, and rural villages. According to Miyamoto, one of his most memorable experiences was the discovery of a cave entrance in the middle of the woods. After some hesitation, he apprehensively entered the cave, and explored its depths with the aid of a lantern. Miyamoto has referred to the creation of the Zelda games as an attempt to bring to life a "miniature garden" for players to play with in each game of the series.
Just as there are multiple Links, there are multiple Zeldas throughout the series. Generally close in age to her respective Link, Zelda is most often portrayed as a child, but has been portrayed as a teenager or young adult on five occasions: in Zelda II: The Adventure of Link, The Legend of Zelda: Ocarina of Time, The Legend of Zelda: Twilight Princess, The Legend of Zelda: Skyward Sword and The Legend of Zelda: Breath of the Wild.
In Breath of the Wild, Zelda rides a White Stallion commonly ridden by her family as a symbol of their divine right. Though her horse is tame it is implied Zelda treated him poorly as she notes to Link she felt that he had to earn the privilege to wear all the Royal Gear. However Link advised her on how to soothe her mount which improved Zelda's relationship and bond with her horse. In an attempt to be more empathetic Zelda equipped her horse with the Royal Gear which she was pleased to discover he wore like a true natural and thanked Link for his advice while riding on Safula Hill. According to local legend, her horse fled to Safula Hill after the fall of Hyrule Castle presumably due to the fond memories it had there of its mistress and the clear view it gave of Hyrule Castle where Zelda sealed herself with Ganon. Toffa implies Zelda's Horse fathered offspring and that the White Horse Link finds their is the grandchild of Zelda's Horse. Zelda is shown riding a White Horse after Ganon's defeat though it is unclear if her original horse was revived/perserved by Malanya or if its the horse Toffa believes to be its descendant.
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.