You have a finished document and it needs something in front of it. There is no need to go back to whatever produced the original.
There is nothing special about a cover. It is a separate single page document that happens to go first, which means the whole job is merging two files in the right order.
Match the page size. A cover made at Letter size in front of a document in A4 gives you a PDF where page one is a slightly different shape from everything after it. Most readers will not notice on screen and every printer will.
Keep the cover as its own file. If you produce many documents with the same front page, having it saved separately means the next one takes ten seconds.
Yes, add it second in the merge order rather than first.
No. Merging copies pages across without altering them.
No.