The overwrite prompt only appears if you're downloading a file and you already have a file that has the same name. It doesn't necessarily mean you "have the same file", it just means you have a file named that. Two files can be the same and have different names, in which case the green check mark will appear, but LimeWire won't warn you that you're going to overwrite an existing file.

If you're not seeing stars on items that have the same name as something in your saved directory, it may be because there's a small delay in updating what LimeWire knows as "saved". For the most part, it should be right, though. Is this a very common occurance?

Torn paper just means you have an incomplete download which matches that file. I think the checkmark (saved) takes priority over that, though. Same thing with downloading (except it means you have an active download).