Can I easily delete apps I don't use from OS Yosemite without damaging other apps? To free up disk space, I'm asking if it's possible and safe to remove some apps from my Mac OS X Yosemite download that I never use. If "yes", how do I do this safely and, hopefully, quickly.
The short answer is: Yes, you can delete apps without "damaging" other apps.

I assume by "Yosemite download" you mean your original full download of the Yosemite operating system and not the "Download folder" only.

The slightly longer answer is: Just go into the applications folder and delete the apps you don't think you need. First, make sure you go into the Mac App Store and credit any possible apps to your account, though. This way, you can delete iMovie for example and later just re-download it from the Mac App Store if you need to.

Deleting an application from the Applications folder will not damage any other app, but I wouldn't recommend deleting anything from the "Utilities" folder.

The bigger problem is that for example Garage Band (if its installed) also has templates and other things installed in Library folders, which also take up quite a bit of space. I wish Apple would allow a bit more flexibility during installation.