BuddyPress.org

Have a look at the functions in bp-core.php, bp-core-templatetags.php :

You can call functions such as bp_core_get_username, bp_core_get_user_displayname, bp_member_avatar, bp_member_profile_data

There is a list of template tags being developed, (https://codex.buddypress.org/developer-discussions/buddypress-template-tags/), but I tend to resort to using find in files in my editor (Coda) and trawling the BuddyPress files.

I understand @johnjamesjacoby is doing work to significantly enhance the API for future BuddyPress releases

I suggest asking your group id questions in a separate thread