That 128GB internal drive presents a bit of a problem.
Not so much for the downloads issue because you can simply create a "Downloads" folder on the external drive and point your browser(s) to that as the default folder.
As for apps... this will be a bit more complicated as most apps really really want to be installed into the Applications folder in the root directory of the startup drive. You can get away with installing some apps in another location such as a folder on an external drive, but others, not so much.
Unfortunately, you've bought a Mac mini with a severely under-sized startup drive, and unfortunately the 2018 mini (macmini 8,1) internal drive cannot be upgraded.
You may be able to free up some capacity by moving your Photos and Music libraries to an external drive, but it won't be long before that 128GB internal drive becomes too full regardless.
I suggest you simply use your 2TB external drive as the startup drive and leave a fresh copy of macOS on the internal as backup. This would be very easy to setup and much less worrisome as time goes by.
How to use an external storage device as a Mac startup disk - Apple Support