The WA_eCart_Database_PHP.php file isn't used in the latest version of eCart, so you can probably just delete the references to that file on the page causing the deprecated message.
It looks like you have an older version of the PP_ECO_PHP.php file (listed in the errors)... I'll attach the latest version, you may be able to just upload and overwrite that one to fix the problem.
The last issue looks like a variable scope issue. open up the waue_pp_confirm_2_body.php file and add this to the top:
<?php
global $eCart1;
?>
I think that will resolve the final error.