There are multiple AV**/security software entries and Trusteer is still detected by PCP, most odd as in your reply #9 29 May 2015 you post that Trusteer had been removed and no more crashes had occurred since, the removal of the multiple AVs was suggested in my reply #30 dated 14 June 2015 and you advised in your reply #32 on 16 June 2015 "I did the steps as above, but Windows Update still isn't working.
" the dates below suggests that Avira may have been uninstalled and then reinstalled while the other security softwares appear to have not been uninstalled as suggested, with the exception of Trusteer any one of the other security softwares could be blocking the Windows updates.
** ESET is not listed in the Speccy logs else that would also have been suggested for removal.
Avira Antivirus
(15.0.11.574)
Avira Operations GmbH & Co. KG
6/16/15
Avira
(1.1.39.17987)
Avira Operations GmbH & Co. KG
6/15/15
McAfee SiteAdvisor
(3.7.228)
McAfee, Inc.
5/21/15
Trusteer Endpoint Protection
(3.5.1412.176)
Trusteer
5/9/15
ESET Online Scanner v3
5/5/15

ESET Online Scanner v3
5/5/15
I would suggest that you try the following, create a new restore point,removal all of the above entries, run CCleaner (free) to make sure that all traces of each are gone, download/install MSE and then try to update the computer, if still no joy try the Fix WU Utility v 1.0 tool from here, please disregard any other product or service that may be offered there and as always be sure to create a new restore point before running Fix WU.