What is safe to delete in order for system to work properly?
Most of the applications you'll delete are going to be restored the next time there is a software update, and even still it'll only save superficial amount of space. For example, the Mission Control, Launchpad, Dashboard, Time Machine, etc. apps are all less than half a meg, and only serve as links to call upon these features via Dock or Finder.

If you want to make a substantial cut on space without making your mac bulimic, i suggest Monolingual, which deletes unused language support (which is usually around 500 MB to 2 GB) and redundant app binaries.

Most Mac apps are "universal," meaning they support both Intel and (the older) PowerPC processor architectures, by having every application contain a binary compiled for each. If you're running an Intel Mac, monolingual can be used to delete the unused app binaries, saving 1-2 GB