Hey,
1) You can update the postRegister method app/Http/Controllers/Web/Auth/AuthController.php file and log the user with Auth::login($user); before the redirect.
2) You can do it by modifying the handleUserWasAuthenticated method in the above-mentioned controller and by replacing
return redirect()->intended();
with
return redirect()->to('your url here');
3) It is not recommended to delete the password confirmation field since it is a standard way to make sure that users entered their password correctly but, if you want, you will need to update the resources/views/auth/register.blade.php view file and remove it manually.
Also, in this case, you will have to update app/Http/Requests/Auth/RegisterRequest.php validation rules and remove the confirmed rule for the password field.