A couple of questions.

[tranceking26]

1) Is it safe to delete these files, or will there be problems with the iPhone backups? (see image below)

2) Is it normal for macOS SSD space to fluctuate for a while? I've been cleaning up old files etc, and once finished it's been going from 80 GB to 70 GB to 65 GB etc. Is this an indexing thing?

 

[Gregg2]

1) Once installed, the installer can be deleted. If you need one again, download it again.

 

[jdw13]

On your second question, you could get info on the SSD drive and see if the amount of purgable space is the culprit.
Since the purgable should b included as "Available" in this output, then than would seem doubtful, but worth a look if you are curious.

I don't know about fluctuate, but I run Mojave (latest) on a 2014 MacBook Pro with a 128 GB SSD, and the purgable space appears to not clear by itself. I am not sure if this has ever caused any me an real issues but it seems to confuse some utilities (like TechTool Protection) into warning me that I am nearly out of available disk space.

Sometimes I'll have almost all of the available space taken as purgeable, and I get the purgable back down by creating/deleting a large file.
If the purgable is less than about 35GB, this can be done with
1)
$ head -c 36000000000 < /dev/random > ~/Downloads/myfile
2)
$ rm ~/Downloads/myfile

It does not matter that "1)" tries to take more than the "Available" listed in the "Get Info" since it will abort when then SSD is nearly full, but
the dummy ~/Downloads/myfile is still there and needs to be deleted.

I would image cleaning out purgable space is not done in nightly/weekly/monthly UNIX maintenance on MacOS in order to keep files in purgable available for recovery?

 

[Taz Mangus]

This helped me with removing the purgeable space.

MacOS How To Remove Purgeable on Hard Drive – JackenHack

Got a "Purgeable" portion on your Macintosh MacOS that you can't get rid off? Here's an easy guide on how to remove it.

www.jackenhack.com

 

[nobullone1964]

Time Machine leaves local snapshots on your system drive. If I recall correctly, once you do a backup that space is regained and the process repeats building snapshots until the next backup. If you google "remove time machine snapshots with terminal" you'll see how to delete this space. Depending on the number of snapshots the tediousness of deleting each separately is a pain. I use Cocktail to thin and delete them easier and faster. I watched my drive go from 700GB to 800GB. That's a lot to gain back. I'm actually looking for a way to disable the function.