Welcome to our forum, I am sorry you are having difficulties using webmail. I have done my best to replicate the issues you mention but do not seem to be able to do it. I logged into one of our test accounts on one PC, changed to list view and logged out. When I then logged into the same email account on other PCs the list view was present each time.
If I view an email in list view it expands to fill the screen, if I then click on the "back" word or "arrow" or delete it (sorry I am not sure what you specifically mean by close)
I am returned to the list of emails.
Are you still having problems, if so would you care to elaborate please.
Interesting I wonder what is going on, I have just tried it with Google Chrome and it is working fine, it remembers list view and if I delete an email in the reading pane or in the list it returns to the list view. I did wonder if it was a setting but I am unable to see one that looks relevant, please feel free to double check them by the way. Perhaps it is worth trying to delete browsing history and cookies on Chrome or even trying another browser Firefox.