'capacity: 111.47 gb, available: 2.7 GB, Used: 108.77GB on disk' - helps confirm your concerns, and original posts' 'Subject' (of 'Full Start Up Disk').
'picture folder: 2.02 GB, music: 359.7 MB, application folder: 7.27 GB total' - confirms that not too many files (data and applications) were added / created on your part.
The 'Terminal' result of 'total 8, 0 drwx ... Send Registration ->' was not of the '/var/vm/' folder; but, of the current users' Home folder.
Navigate to the '/Users/' folder, click once on the current users' Home folder icon, and perform a 'Get Info'. If the 'Size:' value is much larger 5 GB - you may then have to do a 'Get Info' on each of its sub folders - until the folder(s) with the excessive and / or large files is / are identified.
Go to the '/Library/' and '~/Library/' folders clicking on the respective 'Logs' and 'logs' folder, and perform a 'Get Info' on each. Open each folder (and all respective sub folders) and view all the log files. Note if any are quite large. Log files under 100 KB are common; log files in the MBs or GBs are uncommon.