Thank you, these are great questions -
1. That is correct. Four items is the Max.
2. Left vague on purpose. You do not NEED to roll at the entrance but you can and this is helpful with completing missions or bounties because it gives you another opportunity.
3. You do not, but you may continue traveling around and having encounters if you haven't met the mission goal but you've explored the entire map.
4. Once you succeed with a trap that room is free and clear. So you don't have to roll again. However, if you failed the initial roll you have to challenge it again if you return. If you're re-exploring a map then you'd treat the area as new and roll for a new encounter (if you haven't met the goal).
For that situation you mentioned, go with the feel of your story. If it seems odd for a trap to spawn but you ARE supposed to encounter some kind of danger - treat it as an enemy encounter. In some locations that'd make more sense (thinking of Security Building or Freedom Zone). Others, I'd say a really pissed off facility or employee would go nuts with traps trying to keep you from advancing (Laboratory or Orbital Station). However, it depends on your, the player, view of the genre and that makes it interesting.
I'm so glad you're enjoying it! It's one that I've always wanted to return to. There's a lot of fun to be had.