We don't really know for sure how old the dad is. It's not a detail that's focused on in the story. But if I had to take a stab at it, I'd say he could be in his mid to late 30s.
The 'a grand old tree story' could be about a very old tree in the forest. This tree might be home to many animals like birds and squirrels. It has stood there for a long time, through different seasons and weather changes. It could have a magical quality in the story, like being able to talk to those who are kind - hearted and listen to their secrets.
I'm not sure specifically as I haven't read it. But generally, it could be about the life of an old tree, perhaps its experiences over the years, the animals that live in it or around it, and its significance in the local environment.
An old dad I knew was a big fan of baseball. He took his son to every baseball game in town. They would sit in the stands, eat hot dogs, and cheer for their favorite team. The old dad's passion for the sport rubbed off on his son, and it became a great bonding activity for them. It was a story of a dad sharing his love for a sport with his child.
Maybe it's just part of the story's character design. Sometimes, the age of a character is chosen to add a certain element or create a specific dynamic.