Wordpress - Add multiple custom fields to the general settings page

Well the second bit of code is technically the correct way to do it. However, at the end of the add_settings_field() you can pass arguements.

Please view the WordPress Add_Settings_Field function reference. This will help you in getting the best understanding of how the add_settings_field() function really works.

Now, with that said, you could use a 'shared' function for your callback. Such as I do in my options page when I develop themes.

Here is an example of how I do it.

// My Example Fields
add_settings_field(  
    'tutorial_display_count',                      
    'Tutorial Display Count',               
    'ch_essentials_textbox_callback',   
    'ch_essentials_front_page_option',                     
    'ch_essentials_front_page',
    array(
        'tutorial_display_count' // $args for callback
    ) 
);
add_settings_field(  
    'blog_display_count',                      
    'Blog Display Count',               
    'ch_essentials_textbox_callback',   
    'ch_essentials_front_page_option',                     
    'ch_essentials_front_page',
    array(
        'blog_display_count'  // $args for callback
    ) 
);

// My Shared Callback
function ch_essentials_textbox_callback($args) { 

$options = get_option('ch_essentials_front_page_option'); 

echo '<input type="text" id="'  . $args[0] . '" name="ch_essentials_front_page_option['  . $args[0] . ']" value="' . $options[''  . $args[0] . ''] . '"></input>';

}

It will take a little bit of customizing to fit your needs, but doing a shared function for your callbacks will save a lot of space in terms of code. Other than that, you are doing it correctly as is.

--Edit--

Ok, this is what it should be like for you.. just modify the code as needed, I wrote this on the fly.. I did test it to check, and it worked. You just need to modify the add_settings_field(s) to suit your needs. If you need to add more, just copy and paste one and edit it. Make sure to register_setting or it will not work.

add_action('admin_init', 'my_general_section');  
function my_general_section() {  
    add_settings_section(  
        'my_settings_section', // Section ID 
        'My Options Title', // Section Title
        'my_section_options_callback', // Callback
        'general' // What Page?  This makes the section show up on the General Settings Page
    );

    add_settings_field( // Option 1
        'option_1', // Option ID
        'Option 1', // Label
        'my_textbox_callback', // !important - This is where the args go!
        'general', // Page it will be displayed (General Settings)
        'my_settings_section', // Name of our section
        array( // The $args
            'option_1' // Should match Option ID
        )  
    ); 

    add_settings_field( // Option 2
        'option_2', // Option ID
        'Option 2', // Label
        'my_textbox_callback', // !important - This is where the args go!
        'general', // Page it will be displayed
        'my_settings_section', // Name of our section (General Settings)
        array( // The $args
            'option_2' // Should match Option ID
        )  
    ); 

    register_setting('general','option_1', 'esc_attr');
    register_setting('general','option_2', 'esc_attr');
}

function my_section_options_callback() { // Section Callback
    echo '<p>A little message on editing info</p>';  
}

function my_textbox_callback($args) {  // Textbox Callback
    $option = get_option($args[0]);
    echo '<input type="text" id="'. $args[0] .'" name="'. $args[0] .'" value="' . $option . '" />';
}