That is quite a huge ask! It all depends on how the login is implemented, whether there are any rate-limiting firewall/software like Cloudflare, how the search and download endpoint/route is done, etc.
Usually to automate something like this you’ll need a specialised app running selenium to run in an actual web browser to perform the inputs/clicks/keystrokes, and you won’t find a Make app that can do that in a single operation.
If the external service has a Developer API Reference/Documentation, you should be able to integrate the endpoints in Make using the generic HTTP “Make a request” module.
Without knowing more details, we are unlikely to be able to provide further advice.