A PDF carries a set of properties next to the pages: who wrote it, which program produced it, when it was created and last saved. None of it is visible when you read the document, and all of it travels with the file.
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There are usually two copies of the same information: the document information dictionary and an XMP packet, which many editors also fill with an editing history. Pages and pictures can carry their own metadata streams, and some applications keep private blocks of their own inside the file.
Removing metadata rewrites the file without those entries. The pages are untouched: text, pictures, links and form fields stay exactly as they were, and the document still opens in any reader.
The check runs on the copy, not on our intentions: it is reopened, its properties are read again, and the XMP packet is searched for the values that were there before.
No. Only the properties and the XMP packet are removed; the pages themselves are written unchanged.
It can be — in a signature block, a footer or a comment. Those are found separately as personal information, and you decide what happens to each one.
The producer is whichever library actually wrote the file. A word processor, a browser print dialog or a scanner app all leave their own name there.
It is inspected and reported, but no copy is made: this version does not strip the restrictions an author set. You will see what the file contains, with a clear note that nothing was rewritten.