You should use the native (core) comment_post WordPress hook and do the customization. More info here: https://developer.wordpress.org/reference/hooks/comment_post/

I want to display notifications about replies made to my comments, or other comments made for the post.

I checked the actions and filter hooks, but what I really need are functions() that query some of this data.

Is there any documentation about those kinds of functions?

Thanks for the great plugin....

Tom