These days firmwares are not read only and you can download and apply updates to it from the web. So is it possible that if I download firmware from an un-trusworthy site, it might actually have a firmware virus? And if that is possible, how do I wipe out the current firmware on my system and install a fresh copy of firmware?
It certainly is possible, so only download firmware (and drivers and upgrades for apps that came with your device) from a trustworthy site. That does not mean your PC (or external device) is infected, though. It also depends how the firmware is installed -- if you must execute an application on your PC to install the update, it would be easier to engineer malware into it. If firmware is installed by the external device (e.g. by copying files to a memory card and then inserting it into a camera), it is unlikely that malware was installed on the PC.
There are tools such as PeStudio, http://www.winitor.com/, which analyze executables including DLL's and submits them to VirusTotal, https://www.virustotal.com/, which checks the files with about 50 different antimalware tools. Use these tools to check any downloads.
This is indeed possible.
Since a virus is almost simplest terms is nothing but another program or script written with malicious/infectious intentions - the limits to what can be classed as a "virus" are only really limited to the abilities of a programmer.
Since a firmware upgrade is merely a code-update, a malicious firmware upgrade could easily be written to "upgrade" a piece of firmware with something that would "brick" a device or make it behave badly.
To avoid a firmware virus, ensure that any firmware upgrades you undertake are only downloaded from a reputable source such as a manufacturers website. You can also use DrMoishe's suggestion and use tools such as PeStudio to check for virus content within anything you download.
Also, ensure that you always backup an existing firmware (if possible) before attepting any form of update to allow you the best chance of recovering if needed.