The BuddyPress codex is growing and changing. The list of conditional template tags is one of the most handy references available in the documentation. It lists out all of the conditional template tags available for BuddyPress 1.2+, approximately 50 total.
An example:
bp_is_active( $component ) - checks if a BP $component is active
The conditional template tags reference also gives several usage examples that will help you on your way when creating and customizing BuddyPress child themes. I’d recommend bookmarking this one for future use.