Question: Local network with domain D, user U is member of group G in D.

Windows Server 2012 R2 machine M, also in D.

File F on local disk on M. Entire disk has All permissions given to G.

When U is connected to M with Remote desktop, he can rename F, but he gets prompt "File Acesss Denied", "You'll need to provide administrator permission to rename this file". He can click Continue and cmd is executed.

If I give all permissions to U, he can rename F without prompt raised.

Why this difference exists between U and G? How to give same rights to G?

Answer: 
1. Yes, but this doesn't mean they magically vanish as a whole. They're just deleted and it's still possible to use tools to restore those files.
2. There are multiple things considered here. There can be a time limit issued by the web server as part of the HTTP header for example. Also there's the fixed maximum size for Temporary Internet Files (found in Internet options). Plus it also happens if you specifically tell it to remove them.
3. None, other than always fetching the same files, even if they never change, which might slow down browsing the first time you visit a site during a session. Also this will increase your bandwidth usage.
4. It shouldn't, except the points described under point 3.
Temporary Internet Files are all files that are being downloaded when navigating a website. Included are images and files you downloaded when pressing the `run` button instead of the `save as...` button.

The setting `Empty Temporary Internet Files folder when browser is closed` will clear all these files.

`+` The advantages are that your harddrive won't fill up diskspace due to files no longer being used are deleted.

`-` The disadvantages are that because all the files are being deleted, including images, loading websites next time will be slower and it uses up more bandwidth.

On average, the storage space on the Temporary Internet Files location is not huge, and cleaning only once in a while would suffice, unless you really need your diskspace.

As per your point 2: cleaning either happens by you, or the setting automatically at each close. There are programs that do scheduled maintainance that will clean this as well, including the windows disk cleanup utility, but if they are not running/scheduled to run, the temporary internet files storage location will not be cleared.