1. The question is, is it possible to download 3rd party drivers directly
from Microsoft?
Answer: No there aren't available 3rd party drivers from microsoft.
3rd party drivers are only supported by the hardware's
manufacturer.
2. Or do the downloads always have to go through the "connect to Windows
Update..." function?
Answer: No, you can manually download drivers from manufacturer's
site. But before that, you must have to know the details of
hardware like the make and model of it. Every hardware has
its own specific driver.
Here is a link where you can download 3rd party drivers or
device drivers for free:
http://www.driverneeds.net