the desktop item will not delete or "move to trash"
In Finder, select the item. Choose File > Get Info (or do ⌘I). Look under General > Kind. Does it read "Alias" or does it read "Application (Intel)"?
If the latter, then it is likely that you're not allowed to delete because it's actually open. Quit Safari. Check if there is an item called Safari in your </Applications> folder. (In Finder, you can get directly to the Applications folder using ⇧⌘A -- that's Shift-Command-A.) Check if it's an application. If it is, then you have an unneeded copy of Safari. You can delete the one on your Desktop. If there isn't, them move the one on the Desktop to the Applications folder -- that's where it belongs.
If you're new to the Mac, consult
If you're coming in from the Dark Side, consult
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