I can create folders, but I wonder if it is because I use Mozilla Thunderbox to receive the emails. All I do is right click on the word Inbox and there is an option called New Folder, click on that, name it whatever you want and just move the emails across. If they are in the inbox just click and move over, if they are in the sent box, right click, then on the menu find Move To, highlight your email address which will show up and choose the folder you've created. It's very easy.
To save to My Documents, I create a new folder wherever I want it, then with the inbox open (or the send if that's where the email is you want to save), click on File on the top left hand corner and file as usual.
You can then delete the emails from inbox or sent etc. but you'll have them saved somewhere else. Of course, if you delete emails without saving them and even delete from your bin, which I've done, you can always log into gmail and go to all emails and you'll find your lost emails there.