I hate dumb Recruitment Counselors!!!
Well, I don't know if she was dumb or intentionally deceitful. Either way, it's BS that she told you the "computer would freak out" if you only put 2 choices. Not true in the least. You deserved honesty.
Definitely let the Greek Life Office know about your situation. It won't change your situation, but it might make them reconsider their Recruitment Counselor training, whether the RCs simply need to be more knowledgeable or if there is a "you MUST rank all the chapters so we can place every PNM no matter if some are unhappy" attitude. Maybe your story will prevent this from happening in the future.
There is still no way you'd be able to do informal recruitment in the spring. The only thing you might be able to talk Greek Life and/or 3rd choice chapter into is you wanting to reaccept your bid to 3rd choice chapter if possible. That is, if there is still space available. One year my chapter had a girl drop out the day after bid day (we made quota so there was only one spot), and we filled her spot with a PNM who had dropped out after pref.
ETA: Your other questions do venture into the realm of membership selection, and you'll never know how any chapter does it other than the one you're in. It's doubtful that certain members votes count more, but certain people are better at explaining how they feel about a PNM and convincing others to vote with them, so it may be this reason that one may think that certain members' votes carry more weight.
I can tell you that 3rd choice chapter liking you didn't ruin your chances at your 1st or 2nd choices. You were simply not high enough on either of their lists. If you had not ranked 3rd choice chapter, you would have ended up bidless.