Move member icons to header

You cant “move” them. You can create links to different sections of the profile using ##profile_link## as detailed in the Kleo documentation.

You can hide the BP navigation tabs using this css

.bp-user #buddypress #item-nav {
    display: none !important;
}

Keep in mind that you’ll have to remember to add new link to the main menu if you install a plugin that adds a bp profile tab.