Google Ajax jQuery wp_enqueue_script on plugin not working

I have written a custom plugin that should ‘enqueue’ a few .js files into WordPress. The plugin is basically a jQuery Autocomplete that gets the information from a .js file and inject it into Gravity Form input field using CSS class.

I got it all to work, but I have a problem with the “enqueue” of Google’s ajax jQuery file. If I enqueue it in a certain way, the form works 100%, but than it screws around with the admin, especially the “add media” button and the “Visual / Text” toggle buttons on the page.

I’ve tried the “if (!is_admin())” enqueue scripts, but than the form doesn’t work as it should.

So basically, this works, but screws with admin:
wp_enqueue_script('jquery-custom-injection', 'https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js', __FILE__, '2.1.3', 0 );

This is how it should be, but it doesn’t work:

//Making jQuery Google API
function modify_jquery() {
    if (!is_admin()) {
        wp_deregister_script('jquery');
        wp_register_script('jquery', 'https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js', false, '2.1.3');
        wp_enqueue_script('jquery');
    }
}
add_action('init', 'modify_jquery');

My plugin’s main file looks like this:

// registering core Javascript files
wp_enqueue_script('airport-codes-styles', plugins_url('/css/airports.css', __FILE__), '1.0.0', true );
wp_enqueue_script('jquery-custom-injection', 'https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js', __FILE__, '2.1.3', 0 );
wp_enqueue_script('airport-codes', plugins_url('/js/airports.js', __FILE__), '1.0.0', 1 );
wp_enqueue_script('airport-autocomplete-method', plugins_url('/js/method.js', __FILE__), '1.0.0', 1 );
wp_enqueue_script('jquery-autocomplete', plugins_url('/js/jquery.autocomplete.js', __FILE__), '1.0.0', 1 );

This is my first time using a plugin to inject Java files, so I am fairly a noob.