Editing doesn't work when using localized Drupal

You are doing:

if($_POST['op'] == 'Update') {
...
$form['Update'] = array('#type' => 'submit', '#value' => t('Update'));

in easylinks_admin_edit()

Do you see the difference? The HTML button has value "Update", you are checking for "Update". But my Drupal is localized. My button is "Aktualizovat", you are checking for "Update".
"Aktualizovat" != "Update"

This has simple, but maybe not clean solution. Just do

  if($_POST['op'] == t('Update')) {

Instead of previous code. Attaching a small patch, which resolves this in all broken functions. Please note, that the patch includes all my previous patches. But it is small, so it should be easy to merge with your version.