Help: question about external HDD.

Hello, I just get a new external Hdd for my PS4 and I have a few questions about it, so if someone can help:

• When I've instaled the HDD can I move the instaled game on it, or should I un-instal them and re-instal them on the HDD?

• Can I unplug the HDD without any risks (console off, of course) or should I let it plugged all time? I explain myself:

The goal to me is to instal huge game on the HDD, and to plug it only when I want to play those games, while all DL game only or small games will stay on the HDD on the console.

The question is more will the console "bug" or malfonction, if it has game on the external drive, and the said drive not plugged. Of course you won't be able to launch those game but will the console works fine, or will she have troubles search the games/icons on the menu? such kind of trouble...

Thanks for the help.