If I'm looking at that picture correctly, that is the top vac pipe of the
2 vac pipes that connect to the rear of the throttle body.
Is that correct?

If so, then that is the fuel tank vent pipe, (evaporative emission control),
and yes, it should be connected.

If you follow the smallest pipe back, it should go to a small unit
with an electrical connection on it mounted just behind your
cylinder head. Another pipe, the same size, will also come out of that unit
and track down towards the rear of your wheel arch and disappear
inside the wheel arch and out of your engine bay area.

The small white pipe that you are holding with your left hand, is the EGR
pipe, (exhaust gas recirculation), that plugs into your throttle body,
and the other end tracks back around to other side of your cylinder
head where it connects to a large valve which is your EGR valve.

Is all the above correct?

should them 2 black pipes be in together as well the vent pipe of the body ( 1 biger slightley than the other)