First off, your English is great!
Adding PHP to the templates isn't possible and shouldn't be done as it poses a big security risk you don't want to take. Just adding the function rating_form() to the .tpl file isn't ideal. The rating form will display as soon as CuteNews loads the .tpl file, so that will be above the actual news article. Moreover, the rating form won't be displayed for further articles in active news, and I'm sure you'd want to have all news article having the rating form.
What I propose is that you add the code to /inc/shows.inc.php, provided that CuteNews always knows where to find rating_form(), since that's not a standard function. I'm not familiar with the hack, so I don't know which file you had to edit for the additional code.
Basically, you want the rating form to display after every news article? This can be done in /inc/shows.inc.php:
Find twice:
$output = str_replace("{full-story}", $news_arr[4], $output);
Replace both times with
$output = str_replace("{full-story}", $news_arr[4].rating_form($news_arr[0]), $output);
The line is in /inc/shows.inc.php at lines 366 and 695 in an unmodified CuteNews 1.4.6. They're the only two lines that have {full-story} in them - easy to find!
$news_arr[0] is the news ID. I don't think that replacing {news-id} with $news_arr[0] in the .tpl file will work.
Please also note that adding PHP manually to the .tpl files may cause errors in the Templates module of the administration area, and it will be lost if someone resaves the template.