Is it possible to call a template file inside wysiwyg editor? And how?

PHP (unlike HTML) is not meant to be used as content markup language. It is server–side language with too much access. It is very challenging to safely and securely treat PHP as part of content.

For basic example — what if one of your authors writes PHP code in a post which amounts to “make me site’s administrator”?

While WP plugins implementing this do exist, this is almost never good idea, especially at multi–author site.

The typical way of handling more elaborate content in WordPress is via custom fields / meta boxes (/frameworks for both), although it usually falls farther away from WYSIWYG.