That is odd, under the "All" tab you should literally have all of the installed applications including system applications etc. You may want to double check to make sure you were not on the tab to the right of "All".
In regards to the update, yes you can though I would not want to confirm that it will make a big difference to this issue but it can not hurt:
Vivaz? pro - Update Service - Downloads - Mobile phones - Support - Sony Ericsson
Don't worry that is for another phone, the software is the same.