3 Database Errors After 4.1.7 Upgrade

[temsamane]

Please help me with these database errors. What are the reasons of these errors? i think each error has another reason.

error 1:

Database error in vBulletin :

mysql_connect() [<a href='function.mysql-connect'>function.mysql-connect</a>]: Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)
/home/public_html/******.nl/forums/includes/class_core.php on line 314

MySQL Error :
Error Number :
Request Date : Friday, October 21st 2011 @ 10:08:01 AM
Error Date : Friday, October 21st 2011 @ 10:08:01 AM
Script : http://www.******.nl/forums/forum.php
Referrer :
IP Address : support@search.yandex.ru
Username :
Classname : vB_Database
MySQL Version :

error 2:

Database error in vBulletin 4.1.7:

Invalid SQL:

UPDATE vfsession
SET lastactivity = 1319231618, badlocation = 0, useragent = 'Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/535.1 (KHTML, like Gecko) Chrome/14.0.835.202 Safari/535.1'
WHERE sessionhash = '59f010769923f9ba8f21c462243fc02e';

MySQL Error : MySQL server has gone away
Error Number : 2006
Request Date : Friday, October 21st 2011 @ 02:13:38 PM
Error Date : Friday, October 21st 2011 @ 02:14:08 PM
Script : http://www.******.nl/forums/admincp/...?do=dosendmail
Referrer : http://www.******.nl/forums/admincp/email.php?do=start
IP Address : 87.211.145.19
Username : admin
Classname : vB_Database
MySQL Version :

error 3:

Database error in vBulletin 4.1.7:

Invalid SQL:

SELECT text, languageid, special
FROM vfphrase AS phrase
LEFT JOIN vfphrasetype USING (fieldname)
WHERE phrase.fieldname = 'error'
AND varname = 'registeremail' AND languageid IN (-1, 0, 2);

MySQL Error : MySQL server has gone away
Error Number : 2006
Request Date : Friday, October 21st 2011 @ 03:00:07 PM
Error Date : Friday, October 21st 2011 @ 03:00:23 PM
Script : http://www.******.nl/forums/register.php?do=addmember
Referrer : http://www.******.nl/forums/register.php
IP Address : 82.156.55.38
Username : Jack'
Classname : vB_Database
MySQL Version :