The map reads:
If you have running shot, can you running shot into the orange square to do a ranged combat attack out of one of the X's the same turn you running shot?

Also if you occupy an orange square and have RCE on your ship, can you use RCE for an attack made by that ship out of one of the Xs?

Since the map only requires a ranged combat attack, the answer to both of these questions is yes.

Anyone else have an opinion on this?

A ranged attack is ranged attack... I am not sure what other opinion you are looking for.

Sorry for my continued confusion. What I am not understanding is what allows you to combine the use of the attack granted from running shot, and the use of the attack granted by occupying the orange square, into the same action.

On a related note, could someone occupying an orange square, use a running shot action to running shot off an X and do a range attack from a square 1/2 their move away from the X?

Sitting in an orange square (and using its effects) just happens: it doesn't cost anything (no action is given, no tokens are placed, etc to specifically use it).

So if your Ship ends up making a ranged combat attack for any reason while occupying an orange square, the effects will activate. Doesn't matter if that ranged combat attack comes from using RCE, EE, or whatever... just so long as a ranged combat attack is made. And Running Shot, since it grants a free ranged combat action, will cause a ranged combat attack to be made.

No. The ship must occupy the orange square when it makes the ranged combat attack in order to activate its effects.

Got it. And just to follow up on the above question. I think that you cannot running shot from the X while occupying an orange square, because that would require the occupancy of the orange square to allow you to take a power action from the X, and it only grants a ranged attack. Is that correct?

You can't Running Shot from X because your Ship isn't actually in X... it is in the orange square.