It seems that Xojo.Net.HTTPSocket is using the SpecialFolder.Caches folder to store downloaded data.
Before downloading some data from my server I do a SpecialFolder.Caches.Delete to be sure recent (but old) data is gone.
Within the iOS Simulator this is working good.
Running on a device it will hang forever.

What is the best method to delete old cache files?

You can’t delete that folder. You have to delete (carefully) its content

SpecialFolder.Caches is a system app folder were you can put data that will not backupped

Making a folder empty is a piece of cake on OS X.
How do I do that on iOS?

is easier

dim f as FolderItem=<your folder for example specialFolder.Caches> for Each fc as FolderItem in f.Children if not fc.IsFolder then fc.Delete next
In this loop I don’t delete the folderItem if it is a directory

Take care that in the caches folder there is a folder maintained by the system (it’s called as your identifier)