There are plenty of file manager apps available from the Play Store, I prefer 'Ghost Commander' but considering they all have the same basic functionality (with some having more extensive networking features) for the most part it boils down to what user interface you prefer. Just do a search in the Play Store app for 'file manager' and take a look at the screen caps to get an idea on what suits you.
That said, Samsung includes a basic file manager app in their phones so just keep in mind you already have one. Look in your Apps menu for the 'My Files' app. It isn't the most feature-rich file manager but it is perfectly suitable to just move files/folders around and other such basic tasks. (Go into the app's Settings menu and you might find some options to make it more palatable.)
As for some of the specific things you referred to wanting to do, you'll probably find you cannot access a lot of directories as they're system-level protected.
