I downloaded the Falcon package and only 3 of the 4 parts of the package have been fully downloaded. The fourth part, Falcon 4, is stuck at 32.7% . It's been like this for hours. Everything else on the PC is working fine and internet connection is good. Support seems to have gone to sleep. What now?

It's the weekend, which means a skeleton crew at GOG.

Relax, they'll get to it.

I am downloading it with the GOG downloader ...do you mean I should exit it and then restart it? Wouldn't I lose the 32.7% already downloaded? NOTE TO SELF: .."Don't buy stuff on the weekends"

Try downloading it with your browser by logging in on gog.com, then go to your game library and download it manualy. Note that there's a chance it will be slower.
Yes, you'll loose your 32,7% downloaded already. :-(

Yes use your browser and use a plugin that supports download resume like Downthemall, seeing you're from downunder..