The operation is explained in /boot/overlays/README

It is quite safe, I have it on all my Pi in case I need to shutdown a headless Pi (or one without keyboard attached), although my Pi are rarely shutdown, unless I am adding hardware.

I use dtoverlay=gpio-shutdown,gpio_pin=21 so I can shutdown by bridging pins 39/40

Name:   gpio-shutdown
Info:   Initiates a shutdown when GPIO pin changes. The given GPIO pin
        is configured as an input key that generates KEY_POWER events.

…

        This overlay only handles shutdown. After shutdown, the system
        can be powered up again by driving GPIO3 low. The default
        configuration uses GPIO3 with a pullup, so if you connect a
        button between GPIO3 and GND (pin 5 and 6 on the 40-pin header),
        you get a shutdown and power-up button. Please note that
        Raspberry Pi 1 Model B rev 1 uses GPIO1 instead of GPIO3.
Load:   dtoverlay=gpio-shutdown,<param>=<val>
Params: gpio_pin                GPIO pin to trigger on (default 3)
                                For Raspberry Pi 1 Model B rev 1 set this
                                explicitly to value 1, e.g.:

                                    dtoverlay=gpio-shutdown,gpio_pin=1

        active_low              When this is 1 (active low), a falling
                                edge generates a key down event and a
                                rising edge generates a key up event.
                                When this is 0 (active high), this is
                                reversed. The default is 1 (active low).

        gpio_pull               Desired pull-up/down state (off, down, up)
                                Default is "up".

                                Note that the default pin (GPIO3) has an
                                external pullup. Same applies for GPIO1
                                on Raspberry Pi 1 Model B rev 1.

        debounce                Specify the debounce interval in milliseconds
                                (default 100)

sudo echo 11 > /sys/class/gpio/unexport

To disable GPIO pin 11.

How can i switch off the 5V pin? Is there a way?

As Milliways implies, a switch. However, if it's not being used to actually kill the power to the Pi but just the LCD, then you could use the same switch to trigger shutdown (for which you'll need more than just the 5V line connected, which is a bit of a complication, because you can't wire that and a GPIO together on a switch, although a simple voltage divider with two resistors would solve that problem).

Alternately, the "switch" could be an NPN transistor used to control the 5V power to the LCD -- or more precisely, the return to ground (because of the relationship between the collector, emitter, and base voltages).

If you use a GPIO that is by default pulled low, I'm pretty sure (but not 100% positive) that very late in the shutdown process it will go back to that default state, and thereby turn off the power to the LCD.

If not, it is just a matter of setting the GPIO programmatically at shutdown. There's no equivalent of /etc/rc.local for this although I believe cron has a feature that could be used, or you could write a systemd service file with an ExecStart and ExecStop. The former is it seems necessary to the latter, you can't have something stopped that isn't "started successfully" (man systemd.service), but there's probably some way to have something that just runs during shutdown if you dig around. Of course, since you do presumably want to turn the power on at some point, you could use the service for that -- and note "started successfully" could mean at any point, it doesn't have to be at boot.

Anyway, first you need an NPN transistor. These are super cheap (as in pennies) and super easy to use. Unfortunately, you cannot buy just one and they likely don't have any at the nearest grocery store, but what you are looking for is a bag of something like the very commonplace 2N2222.

It seems you are connecting your LED to a power supply and ground, what else should it do but light up (or burn, without a resistor)? In other words, you are not using any GPIO actually.

To be able to control when it goes on you will need to connect to an actual GPIO and then ground or power. You can then control the LED by setting the GPIO you use to high or low respectively. Note that you need at least one resistor (to protect the LED), but probably should use more to provide some protection against using it wrong (which might burn your hardware!). Refer to the various available how-tos on this. An example I like (with good follow-ups) is http://raspberrypi.powersbrewery.com/project-1-a-simple-led/ ...

Keep the fan connected to the 5v pin. Connect the other side of the fan via a transistor to ground. Switch the transistor on and off via a GPIO pin. This will turn the fan on when the transistor is switched on and switch it off when the transistor is switched. There are plenty of web sites with how to do this.