BuddyPress.org

I think you need a child-theme and change the header.php to include your custom navigation, I have created a similar menu but did require a lot of work in the header.

When new messages the number of messages shows in the message-icon, links to profile page, also woocommerce integrated and a dashboard link for admin only.

The following is in my custom header.php

First code links to profile.
<li><a href="<?php echo bp_loggedin_user_domain(); ?>" class="activitylink" title="My Account"><span class="dashicons dashicons-admin-users"></span></a></li>

This code deals with messages.

<li><a href="<?php global $current_user; echo home_url() . '/members/' . $current_user->user_login . '/messages/'; ?>"><span class="dashicons dashicons-admin-comments"></span><span class="commentcount"><?php if (bp_get_total_unread_messages_count( bp_loggedin_user_id() ) > 0 ) { ?> <?php bp_total_unread_messages_count( bp_loggedin_user_id() ) ?><?php } ?></span></a>
</li>

Since I did not want too much in my nav I only used these buddypress features, more would clog up my website too much.

But where it comes down to is with a child-theme you can make it exactly as you like.

Good luck
P.H.