Is it possible, to make backend fields of 'type' => 'text' required with TSconfig?
No, this is not possible. You need to create a sitepackage or extension and put something like this in typo3conf/ext/your_extension_key/Configuration/TCA/Overrides/your_table.php
:
<?php
$GLOBALS['TCA']['your_table']['columns']['your_field']['config']['eval'] = 'trim,required';