I think one of the problems is solved but other one is not.
1) As mta and Digerati said "Continue running background apps when Google Chrome is closed" must be unchecked. But sometimes even you exit chrome "chrome.exe" still resides in background. If so, manually kill the process in windows task manager.
2) Make sure in CCleaner, on the Applications tab in the Google Chrome section everything is checked (maybe except session because if you chek this, then, next time you start chrome, it cannot show you the pages leaved open before exiting chrome, i.e. next time chrome only shows your homepage)
3) Run CCleaner and most visited web sites boxes in new tab window will be cleared.
I think this is the solution for the first problem. Thank you everybody for your help.
But for the second problem, that is, clearing the most used bookmark folders list, I think we have no solution because chrome sync everytime this data from google servers. If you stop sync then your favorites will only be available for that computer. So this isn't a solution for me.