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.