On the last day of October, a greenish grasshopper Phaneroptera nana ...

To be exact that's not a grasshopper. You can read more about the differences between grasshoppers and crickets in this post.

Unfortunately, I haven't been able to determine the species of this mysterious companion yet.

Great pic! To determine the exact species you should start your research within the suborder Auchenorrhyncha and there in the infraorder Cicadomorpha.