Private Instances?

[dishymars]

Im a bit confused hopefully someone whos been playing a long time can explain.

Is it possible to get into a private instance or form a group and get out of the public instance? Example I am supposed to find the construction site and the fear gas canisters but there are just too many people around and its irritating.

Is the whole thing like this? Can you form a group and enter your own private instance? I was looking around the options I didnt see anything.

Is there a grouping board where you can find a 3-4 other players and go on the mission with just them or is the whole thing just public instances?

Thanks