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.
Create a cover in an authoring app and export it to PDF, or convert an image cover with Images to PDF. Put the cover first in the merge list. This tool does not write cover text or renumber existing printed page labels.
Pages are copied without rasterising their content. Merging does not compress the resulting document.
Check document-level forms, bookmarks, links and signatures separately: rewriting a PDF does not guarantee they survive unchanged.
Write the cover in a word processor and save it as a PDF, or use Word to PDF for a .docx file. Then add the cover and the main document to Merge PDF, and move the cover to the top of the list before you press the button. The page total shown afterwards should be the cover plus the document.
If the document is numbered, you probably do not want the cover to carry a number. In Page numbers, use Leave the first pages bare for the cover, and the numbering starts on the page after it.
No. It combines pages. Raster compression is a separate operation and removes searchable text.
A PDF that needs a password to open must be unlocked first with Protect PDF. For a very long document the thumbnails can take a moment, and you can still type the page numbers yourself.
Yes. In Page numbers, set Leave the first pages bare to 1, and set First number to what you want the second page to show.