1) How can we sort the database with pictures? Now new pictures are placed in front of the other photos instead of sorted (alphabetically).

Take a look at the file /include/config.inc.php, it explains how to use the variable $conf['order_by'] in order to display pictures alphabetically without taking into account the date of add to the gallery.

2) How can we delete pictures (without using other software?)?

You can't. You have to use your FTP client software to delete pictures. Then you need to update your database with the script of the admin pannel.

3) Is it possible to place a text on the frontpage of phpwebgallery (a short intro or information of the photo dB)?

Yes, my advise is to replace the default text shown when no category are selected. For this, you have to modify (for each language available of your site) the variable $lang['no_category'] that you will find in the language file, for example in /language/english.php.