"We are going out."
Translation:Wir gehen hinaus.
The first one means that you are going towards the outside and away from the position where the speaker is.
The second one means that you are going outside and towards the position where the speaker is. It makes no sense to me, since the speaker is part of wir and so he can't move towards his current position; also, movement towards the speaker's position is usually described as "coming" rather than "going".
Two possibilities: Ich geh gleich (i.e. I'll be leaving my house soon) or Ich komme gleich (i.e. I'll arrive at the bar soon).
Ich komme jetzt raus would be appropriate if someone is waiting for you outside a locked toilet stall, for example, and you're telling them that you're about to come out.
In meaning, no.
raus is a bit less formal than hinaus, so you might not use that in an academic thesis or something like that; and conversely, in everyday speech you would probably be more likely to use raus than hinaus.
But the meanings are the same. raus is simply a short form of heraus or hinaus.
(It must have originated as a short form of heraus, but is also used as a short form of hinaus. So it doesn't matter whether the movement towards the outside is away from you [you are inside] or towards you [you are outside]; raus works in both cases.)