I had exact the same problem with my
W660. This was caused by one program, wich needed to get access to internet (it was like full version of game, wich periodicaly needed to display ADS screens). At first, my phone got slow and menu did not work correctly, secondly, it had the same annoying things as you have (restarts, white screens, operation failed when trying to delete any of the apps, duplicated apps). Also master reset from menu did not solve the problem and all the apps and annoying things did not disappear. And from that point, I never download anything from untrusted source.

Also I was in hurry to fix my phone, so I did reflash my phone with SEUS (Sony Ericsson Update Service) and it deleted all my stuff (Fortunately I backed up all my contacts, nothing else were important). And my phone is running fine now.

So, In conclusion... Reflash is the only thing that works, you can do it either by SEUS or by using 3rd party flasher programs (wich is harder, but better). I say better, because by using SEUS you will get CID53 and it is harder to customize your phone afterwards (many programs do not support CID53 yet). (But if you are not in need to customize, you can try SEUS).