Will Parallels be safe while upgrading to El Capitan? The new update seems pretty legit, so I am considering updating my macbook. 

I have Parallels installed on my computer, and I don't want it to be removed or damaged during the installation of El Capitan.

If I use time machine to back up my macbook, will it back up everything and keep Parallels and the files on it safe? Or, will it only store original Mac files, ignoring parallels?
If you haven't set Time Machine to exclude any files from the backup, you should be fine.

If you want to be really cautious, you can find the Parallels virtual machine file and manually copy it onto your external hard drive, free space permitting. Put it at the top level of the drive, not in the Backups.backupdb folder.

This will keep your files safe on your external hard drive no matter what happens on your computer. To make sure you can keep actually using Parallels, though, you'll need to make sure you're on Parallels version 10 or 11. Version 9 will not be supported in El Capitan.