1/ You need to create one modal or page template, then you need to add the code of the login form. Please follow the file location, here you will find login form code.

tutor/templates/global/login.php

2/ Here is two way to use different menu for logged in and logged out user. 1/ You can use the WordPress plugin 2/ You can use custom code. Please try this code

function wpc_wp_nav_menu_args( $args = '' ) {
if( is_user_logged_in() ) { 
    $args['menu'] = 'logged-in'; // Replace logged-in with you menu name
} else { 
    $args['menu'] = 'logged-out'; // Replace logged-out with you menu name
} 
    return $args;
}
add_filter( 'wp_nav_menu_args', 'wpc_wp_nav_menu_args' );

3/ Please use the code below

add_action('wp_logout','tutor_redirect_after_logout');
function tutor_redirect_after_logout(){
         wp_redirect( 'Your redirect URL here' );
         exit();
}