It looks like you are missing the Session::start() call in your UserController. This is necessary to start the session and set the session store.
You can add the following code to the __construct() method of your UserController:
public function __construct()
{
Session::start();
}
This should resolve the Session store not set on request error.
For the Undefined variable $errors error, you can add the following code to the register.blade.php file:
@if ($errors->any())
<div class="alert alert-danger">
<ul>
@foreach ($errors->all() as $error)
<li>{{ $error }}</li>
@endforeach
</ul>
</div>
@endif
This should resolve the Undefined variable $errors error.
Hope this helps!