BuddyPress.org

You do not need to do anything or at least shouldn’t. A child theme inherits everything from the parent until the point that you copy a file over to the child theme, however certain files are called regardless functions.php and the global.js files are called regardless. To start with do not do anything with your own custom functions file, leave that until things are working correctly. The mention earlier of the @mentions dropdown sounds like a JS issue not a functions file one so I wonder how you’ve set up the child theme. To actually confirm the base install works please activate bp-default and confirm things work.