Display the connected customer information

I have 2 tables which are user and customer, la first table has like fields following:

(id, name, email, password).

Then, the table 'customer' has like fields (id, name, firstname).

In my Controller Customer, via my function index(), I have to retrieve id_user from my table user.

1 question // is it my relationship is correct between my 2 tables?

Model Customer

protected  $fillable = ['name', 'firstname', 'user_id'];

public function user()
{
        return $this->belongsTo('App\User');
}

Model User

public function customers()
{
        return $this->hasOne('App\Customer');
}

2 question // How retrieve ID of the user which is connected ?

I have for now this only...

public function index()
{
        $customers = Customer::orderby('id', 'desc')->paginate(5);
        return view('customers.index', compact('customers'));
}

3 question // I wait to understand the answer two, but I would like to understand. How I have to adapt my file index.blade.php via my loop please?

@foreach($customers as $customer)
 <tr>
   <td> {{$customer->name}}</td>
    <td> {{$customer->firstname}}</td>

Thank you for your explanations.