Sure.
Let's start with the questions you asked initially.
What are the right questions to ask?
Looks like you already done a great job already with the questions you posted.
How do I learn how my HD filled with System Data?
Again, what "fills" System Data is controlled by macOS. The largest contributor is from Time Machine local snapshots. These are complete copies of your Mac's Macintosh HD - Data volume, and are created hourly. However, TM will remove them daily ... at least, it is supposed to. There are a number of methods to remove them "manually," but you shouldn't have to. One of them is to boot up your Mac in Safe Mode.
Ref: About Time Machine local snapshots - Apple Support
How do I see see what System Data has been stored on my HD?
Since TM local snapshots are the biggest contributor, you can get a list of them by using the following command in the Terminal app: sudo tmutil listlocalsnapshots /
How do I clear it safely?
In one of the following four ways:
- Let macOS perform the work. (Recommended)
- Boot up the Mac in Safe Mode.
- Toggle off; wait 5-10 mins, then toggle on "Backup Automatically" from the Time Machine menu in System Preferences.
- Use the tmutil command in the Terminal.
How do I manage System Data?
Again, it best not to micro-manage System Data, but just let macOS perform this task.
If there are any other questions you may have, related to this, please ask away.