Cloud Function: Deleting from both Firestorage and Firestore in a kind of "batch"
I must admit that I haven't really used firebase or done any android development and thus cannot answer your questions about the correctness of the code. I did wonder if using a transaction would help satisfy the need to prevent deletion of items if other items cannot be deleted, but maybe the batch handles that... Maybe the process to delete the file (i.e. deleteFile) should be added to batch, although maybe that not possible because it is the firestorage document.

Good things

The code makes good use of const for values that don't get re-assigned.

Indentation is consistent and helps readability of the code.

Functions aren't overly long.

There aren't many indentation levels because the first function will exit early in an error state.

Suggestions

I don't see any comments. The code does seem mostly explanatory as it is but it would be helpful to have some insights about the code - at least function parameter types, return types, etc. Over time it might become difficult to remember why you may have done something a certain way.

Many variables are declared and then only used once. There is little point in doing this. Many of those variables can be eliminated - e.g. the_post, promise, stored_image_name, filePath, updateUserLikes. 

The variable name deleteDbEntry could be confusing to other readers of your code. A more appropriate name might be dbEntryToDelete.

The lambda function passed to .then() of Promise.all() could be simplified to an arrow function - e.g. 

return Promise.all([deleteFile, batch_commit]).then(_ =&gt; 1)