1) This will be solved in 1.3 final. Try running this SQL query:
UPDATE `".TABLE_PREFIX."user_ws_config_options` SET
`config_handler_class` = 'BoolConfigHandler',
`dev_comment` = 'Notification checkbox default value'
WHERE `name` = 'can notify from quick add';
2) If you are using another language other than english, (or more accurately, other date format other than 'm/d/Y') then maybe your tasks are being set to a wrong due date, and that's why you don't see them in the week you are looking at. For example, if you are using a language that has a date format of 'd/m/Y' and you set the due date of a task to '1/3/2009'. maybe it is being set to January third 2009. This is because of a known bug when handling dates in OpenGoo's date controls. Could this be the problem?
3) The command should be something like 'php /path/to/opengoo/cron.php'. Maybe the executable you have to use is called php5 and maybe you have to give the full path to the executable. Also, maybe you want to redirect output to a file so that you can check any error messages, by appending a ' >> log.txt'.
4) This has already been corrected and will be available on version 1.3 final.