: Now rise.
Nice finds that I don't recall (except getting caught in the goo trap). However, I think most level designers (at least in the US & such, due to driving on the right side of the road) tend to design levels with the assumption that the player(s) will explore to the right first. I'm getting to my point; soon.
I recently played level 2 and I usually explore by moving toward the left side first. I save when I can in solo, and I found the normal exit terminal and exited to level 3 without having explored even half of level 2. So I chose to resume from the saved game and proceeded to explore the other level areas.
Since you both began exploring to the left after leaving the initial area, you missed the areas on the right side as you left the initial area of the level, which opened up when you hit the first button of the level. Otherwise, it was a cool run through, and Blackstar demonstrated great self control by not just killing every bug on the level. :-)