We have a link that says "Download" so the user can download transcripts.
Please note that these files will be in ZIP format and typically, it's a PDF or DOC file in a zip. File sizes are never going to be large, so we don't think we need to add some sort of progress bar since downloading is typically very quick.
Does this link need to be more explicit? eg, "Download 2 files"
You technically are only downloading the one ZIP file which contains the PDF and DOC, right? In which case "2 files" would be misleading.
Does there need to be indication if the file once download has completed?
Assuming that you're operating in a browser, this is probably more of a nice to have than a "need". Unless you're expecting your users to be extremely novice computer users who visited fewer than a few dozen websites in their life, it can be expected that they have figured this out.
That said, you can validate this expectation by tracking if people download the same ZIP multiple times. In that case, you may need a post-download screen that tells them where they need to go to.
One of the heuristics and principles of good design is to provide clear visibility of system status. In the case of downloading files, it means that the user is clear about these things:
Most of the information should be provided before they start the download, and not all of them will be necessary depending on their download speed or whether the download is successful or not.
