Thanks for your post and suggestions.
1- The possibility by a shortcode modification of the profile avatar
The core plugin relies on WP’s gravatar support. If you want to utilize a custom image locally, there are a number of ways to go about that. One such possibility is to create an image upload field (the plugin allows for image fields) and filter WP’s avatar functions to use that image. That merely requires using WP’s already available get_avatar filter, but I do have a code snippet to demonstrate how to do it.
It is likely that identifying a field as a custom avatar will be added as a field property in a future version. I just haven’t determined if that will be a specific field type or if it will be a property of the image field type.
2- Make certain fields visible on the profile but not on the registration page
That will be added to the Fields tab for selection in the settings in a future version. However, no specific version milestone has been determined at this point.
In the meantime, you can filter the fields that are used for registration, profile, and dashboard using the wpmem_fields filter. There are some example of how to do that here:
https://rocketgeek.com/plugins/wp-members/docs/filter-hooks/wpmem_fields/
3- A shortcode on the last connected members
4- The possibility of becoming friends with other members
5- The possibility of putting a publication “Thread” in his profile visible by other members who can comment on a kind of Facebook profile
These last three are somewhat outside the scope of the plugin and are more in line with a community or social membership plugin such as BuddyPress. Keep in mind also that a membership plugin for content restriction like WP-Members can be integrated and used along with a membership plugin that is more of a social networking plugin like BuddyPress. While I won’t say “no” on these for sure, I will say it’s not likely they’ll be explored in the immediate future.