The "my collection" collection is a default made for every user. I suppose you could delete this collection in mysql, but I'm unsure of how this would affect the rest of the system.
The "b" permission toggles the collection bar at the bottom of the screen. supporting options for restricting collections can be found in the config (what below are taken directly from config.default.php):
# Display a 'My Collections' link in the top navigation
$mycollections_link=false;
# Confine public collections display to the collections posted by the user's own group, sibling groups, parent group and children groups.
# All collections can be accessed via a new 'view all' link.
$public_collections_confine_group=false;
# Show public collections in the top nav?
$public_collections_top_nav=false;
# Allow users to create new collections. Set to false to prevent creation of new collections.
$collection_allow_creation=true;