for how long do the personal messages stay, for example i send message to other person and for how long it will stay in his inbox?
If the source code of the board is not modified then the messages are removed from the database. This is rare these days, most of the web software simply sets a delete flag. In the source code of SMF you can see the SQL queries of those deletes:
// Delete anything related to the topic.
$smcFunc['db_query']('', '
DELETE FROM {db_prefix}messages
WHERE id_topic IN ({array_int:topics})',
array(
'topics' => $topics,
)
);
This makes it unavailable for direct access. The data is still on the drive somewhere until overwritten.
In short, the message is there unless the drive is overwritten.
Source here:
http://download.simplemachines.org/index.php?thanks;filename=smf_2-1_beta1_install.zip