How does Laravel Model Broadcasting deal with private channel auth? And some other questions about broadcasting in Laravel

I'm working on a simple chat web app using Laravel. I've decided to use the Model broadcasting routine here. But I don't know how model broadcasting authorize users. I know the standard method is like:

Broadcast::channel('orders.{orderId}', function ($user, $orderId) {
    return $user->id === Order::findOrNew($orderId)->user_id;
});

While model broadcasting also broadcasts on private channels, the docs doesn't describe if developers need to set up authorization callbacks. So, do I need to create a private channel authorization callback like:

Broadcast::channel('App.User.{userId}', function ($user, $userId) {
    return $user->id === userId;
});

And the second question: can I create different private channels authorization callbacks for different auth guards like:

Broadcast::channel('channel.{memberId}', function ($member, $memberId) {
    // ...
}, ['guards' => ['member']]);

Broadcast::channel('channel.{adminId}', function ($admin, $adminId) {
    // ...
}, ['guards' => ['admin']]);

The last question: does the broadcasting in Laravel support client-to-client broadcasting? Because I need to limit who can send messages to specific channels, if the client-to-client behavior exists it may effect the privacy of users in my app.

My native language is not English. Sorry if my words are not clear.