Sure. 'The finale', 'wrap - up' and 'cessation' can be used instead of 'end of story'.
Yes. You might use 'final curtain', 'completion' or 'termination'. 'Final curtain' is often used in the context of a performance or show coming to an end, but it can also be used metaphorically to mean the end of any sort of story or situation. 'Completion' emphasizes that everything has been finished or accomplished, and 'termination' has a more final and perhaps a bit more abrupt sense to it.
Wrap - up. This is a more informal way to say the end. Just as a movie or a project has a wrap - up at the end, when you say 'wrap - up' in the context of a story or an explanation, it means it's over. For example, 'So, that's the wrap - up of what happened yesterday.' It's a handy alternative to 'end of story'.
Bedtime narrative.
Life chronicle. A chronicle is like a record of events in the order they occurred, so a life chronicle would be a record of a person's life events over time.
Recounting a tale.
Built on a factual event.
In stories, 'lengthy duration' is a good alternative for 'long time'. Let's say in a science - fiction story about space travel, the journey might take a lengthy duration. 'Substantial period' is also a possibility. In a detective story, the investigation could take a substantial period of time. Additionally, 'extended time frame' can be used. For instance, in a story about the evolution of a species, it might occur over an extended time frame.
Climax. Although the climax is often near the end and is the most intense part, it can sometimes be considered as leading to the end of the story.
Denouement. This word specifically refers to the final part of a story where the plot is unraveled and all the mysteries are solved.
There are expressions like 'weave a tale' and 'construct a story'. When you 'weave a tale', it's like you are carefully putting together the different parts of the story as if it were threads in a fabric. 'Construct a story' gives the idea that you are building the story from different elements, like building blocks. These expressions are a bit more creative than just 'tell story'.