I play this a little different....
1st, I think that there is a window in the space, directly in the center of the floor. The rope hangs from the "ceiling" of the room. Remember that the rope can be anywhere from 5' to 30' long....
So, as long as you are touching this piece of rope, then you are fine... NOTE: this spell will not work on 50' of rope... so IMC, the rope is an additional material component of the spell.
Now, the window is open, no matter what. You can't close the window. It is a window that you cannot see through from the caster's plane of existence, but can be seen through from the extradimensional space side...
This window is Invisible. That means that if you can see invisible things, you can see the "open" window, just not through it. So this means to me, that you can target "through" the window with objects if you wish, if there is space within the extradimensional space...
To me, that means that there is room for 8 things in the space. These things can be people (and all they carry) or objects, which is why the rope takes up one of these "spaces."
So, if the rope trick is full (has 8 things) in it, then the window is effectively closed, and will not allow other objects to enter it. If the space is not "full" then other objects can pass through the window to the occupants.
Ok, so that means you can fire or throw an object through the window... cover would apply to those within, as well as a 50% miss chance if you taget the right square. What I typically do is draw a block 3 squares to the side. The center square is the window. Place PC's or objects in each of the blocks. If the shooter/thrower can "see" invisible objects, or can see the rope in the window, or even has knowledge of the spell and its effect (Spellcraft), then they can try to shoot/throw through the window to effect the inhabitants of the space.
Spell effects will not cross the window boundary and don't forget the extradimensional space within an extradimensional space problem... And for DM's sake, don't tell them about that problem!!!!
Aluvial