Short answers, pulled from the story.
The King Kong Show, produced in the late 1960s and early 1970s, is one of the first noted attempts by an American company to make a visually anime-inspired series. It was the result of a collaboration between Toei Animation in Japan and Videocraft in America, blending a Japanese kaiju theme with the art style of the Hanna-Barbera era in American TV animation.
Yes. Creators Bryan Konietzko and Michael Dante DiMartino confirmed anime influence in a magazine interview, naming Hayao Miyazaki specifically, including Spirited Away, Princess Mononoke, and My Neighbor Totoro, as well as Studio 4°C, Production I.G, Polygon Pictures, and Studio Ghibli as studios that inspired them.
RWBY is a web series produced by Texas-based company Rooster Teeth that premiered in July 2013. It uses a heavily anime-influenced art style and was referred to as American anime by multiple sources, including a publication that used the headline "American-made anime from Rooster Teeth gets licensed in Japan" when the series was licensed for release in Japan. In 2022, RWBY received an actual Japanese anime adaptation called Ice Queendom.
Disney animator Glen Keane described Miyazaki as a "huge influence" dating back to The Rescuers Down Under in 1990. Pixar co-founder John Lasseter traced his engagement with Miyazaki to first seeing Castle of Cagliostro. The Lion King director Roger Allers stated that Doraemon, which he saw in Japan before 1988, greatly influenced the film, and Fujiko Fujio thanked Disney for the praise in 1995.
The Canadian animated short Flutter, made in 2007, became the first work from a non-Asian nation to win the Open Entries Grand Prize at the Tokyo Anime Awards. A year later, Chile's Nahuel and the Magic Book became the first Latin American feature to win the Tokyo Anime Award for Award of Excellence.
Murakanime is a style associated with animator Glen Murakami, who worked alongside Bruce Timm on Batman: The Animated Series and Batman: Beyond before collaborating with producer Sam Register on the Teen Titans television series in 2003. The term refers to the blend of sharp-edged American superhero design with cyberpunk, science-fiction, and Japanese visual elements that Murakami brought to the projects he worked on.