Apple - Deleting files for freeing the disk space

Honestly delete nothing in those directories manually. You'll likely crash your system if it even lets you delete them. Stick with files in "userland." which would be at the path /Users/[YOURUSERNAME]/."

If you are running out of disk space (which is completely different from running out of memory) I would use a gui tool like Grand Perspective and then delete the files that you no longer need that occupy locations in your user directory.

I'm sure there are shell commands to list, recursively, files in specific directories in order of file size, but I don't know how to do that, preferring GUI tools that do the same thing.

If you are running out of memory in your MBA then the only choice you have (as all MBA memory is non-upgradable) is to see if you have a bunch of things running at startup (system preferences > users > [YOUR USERNAME] > login items) and remove some of them or just run fewer apps at the same time.

The sleepimage file can safely be deleted by the user. It will be recreated the next time the Mac is put to sleep due to a default setting which can be disabled. This page at TechRadar shows how to delete the sleepimage file, as well as how to disable the recreation of the file.

The sleepimage file is a snapshot of the contents of RAM taken just before the Mac is put to sleep. When the Mac is awakened, this file is used to recreate the RAM contents, ostensibly to make the process quicker.

Swapfiles will always be created, and there's little you can do other than increasing the amount of physical RAM in your Mac.

Please edit your question to indicate if you are asking about RAM usage, or if you are getting Startup Disk is Almost Full messages.