Can Inspiron 3471 support a 3.5-inch 16TB hard drive?

Yes, your computer supports SATA AHCI protocol, which is a modern standard for SATA storage controller.  It will support any standard SATA drives available in the market, including a 3.5 inch 16 TB hard drive.  Capacity limit from Dell specification is for tested and validated products available for system purchase.

Storage specifications  https://www.dell.com/support/manuals/en-us/inspiron-3471-desktop/inspiron-3471-setup-and-specifications/storage?guid=guid-90355540-ea93-4e6a-a60a-8e1b03c7cb3c&lang=en-us

Thanks for your information.

One more question, my computer only equipped USB 2.0 inputs.  If alternatively I would like to connect an external 16TB HDD through USB instead, is there any simple way to upgrade the computer to USB 3.0?

Beside four USB 2.0 ports, your Inspiron 3471 also comes with two USB 3.1 Gen 1 ports.  The two blue USB ports located at the front panel.  See ports #9 in picture below.

It's possible to add USB ports to a desktop PC.  Normally, users can add multi-ports USB add-on card to an available PCIe slot.  Inside your PC, besides one PCIe x16 slot being reserved for video card, there is an extra PCIe x1 slot that can be used for such expansion.  Other method is to add USB 3 hub (preferably powered) to an existing USB 3 port