Old Yeller is fiction. You can tell because it has elements like a made-up plot and characters that aren't real people from history or actual events. It's a wonderful fictional tale though!
Yes, it can be considered realistic fiction. It portrays a story that feels true to life and deals with common themes and situations that could happen in reality.
The climax is when Old Yeller has to fight off a rabid wolf to protect the family, but gets bitten and has to be put down by the boy who loves him. It's a heartbreaking and intense moment.
In a way, it was. The story of Old Yeller has elements that draw from common human-canine bonds and real-life situations, but it's not a direct retelling of a specific true event.