Is it possible to clear the storage of a game saved by the System object (-> System: Save game to slot "x")?
There is no direct way to delete data from a save slot.
The most straightforward way is to overwrite the slot with a new or fresh game state.
Normally what you would delete is the reference to that save slot, so users can't pick it anymore. In other words rather than deleting the save slot, you can delete the ability for a user to load a particular save. You do this simply by setting a new slot to save to and load from, and you can overwrite the old one at a later time if you want to save space.
Or is it possible to save and load the entire game in a LocalStorage as simple as "System: Save game?"
It is possible, but not simple at all. You'll need to manually determine everything to save and load. Depending on the type of game and how much data needs to be saved, this may not be feasible.