Your files that keep reappearing are due to the fact that they still have the apps installed that are associated with them.
The first 2 folders are from Picasso - which is an image download service, and does more than just that. Its a very important part of the Android OS. Without this and things don't work right, unless you find a replacement that will integrate with the system. Volley and Universal Image Loader are the other 2 contenders that come to mind. Getting rid of those folders isn't an option for you.
The last one, /7zlogs, is associated with a compress/decompress app. It is a folder that hold the log files from the app. You should be able to go into the apps settings and turn off logging. Once done with that you can delete the folder without the chance of it reappearing.
Be careful of what you delete, ALWAYS do a backup before messing with anything