Going to the ASUS website and typing "Q524UQ" quickly directed us to the desired page designated for our device.
Clicking on "Driver & Tools" prompted us for information regarding our laptop.
In order to find the location of the system model, we looked into System Summary in System Information.
Clicking on the link labeled "Global", we downloaded the zip file containing the BIOS update file.
WinFlash is a program that came pre-installed on our Asus, and is the tool to use in order to update the BIOS.
We then were presented with two options; Get BIOS from the Web, or Get BIOS from Device. Turns out, it was really just one option, as clicking on "Get BIOS from the Web" results in a prompt telling us to manually download the file from ASUS' support site.
Having done this earlier, we could quickly locate the file in our downloads folder and unzip it.
We returned to WinFlash and select our newly unzipped file as the source for our BIOS update.
However, our BIOS appeared already already up to date.
Moving on to Thunderbolt, we found a file in the "others" folder on the same page as the BIOS file on Asus' support site.
This time we did not use the WinFlash software, as the zipped file included an application, presumably used to update the Thunderbolt firmware.
Initially, we were unable to open the application for unknown reasons. Multiple attempts were made, mainly through double clicking on the application file. We saw indications that something was loading, but no new screen popped up to allow us to continue.
We tried running the same software the next day and this time, the application opened and ran successfully.
The application gave us three options: change, repair or remove installation. We chose remove installation.
After removal, the application installed the new Thunderbolt Firmware version.
Overall, the process of updating BIOS and Thunderbolt Firmware the Asus's Q524UQ was pretty straightforward, although with some hiccups.