Can you start installing a game update without having the actual game?

No because the install file has to be triggered by the game file.

How can you install an update for something that you don't own? SERIOUSLY! What's the point trying when such data is irrelevant for your system (as all you would be doing is just wasting HDD space)?

Until you have an actual copy of the game (whether you actually purchase a copy of borrow a copy from somebody), you will not be able to pick up any updates for said game. Your system's online store will prevent you from downloading anything that has a prerequisite which you do not have covered.

Nope, the PS4 won't check for an update for something unless you have used it before. Now you could borrow the disc from a friend, load the game once, give the disc back, and you should be able to check for updates and install them from the main screen where it shows your recently played games. At least I know I've updated Shadow of Mordor recently although the disc hasn't been in my PS4 for months (but I've only played one or two other games since, so it shows as something recent).

You can if you buy the game download from the PS Store. The game will download prior to the release time and will be unlocked when the release time arrives.

no you need to have the game to update it

nope

No.