I too was taught only to fall if the nage makes me need to, don't be stiff, don't force resistance (with an unwritten "unless you're a pair of yudansha testing each other's response"), but there's one exception I'm curious about that I haven't gotten around to asking sensei about yet. Anything that involves a throw into rolling ukemi, you roll no mater what, even if the person didn't successfully throw you. I'm guessing this is partly for safety, partly for practice doing rolling ukemi well? It usually manages to still be obvious to the nage and the sensei if the throw wasn't good.
Depends. With a newbie I take the roll. With somebody else depending on their skill level and other factors....I may follow their energy even if my balance isn't fully taken and let us make the roll happen OR ... I may go where they are actually putting me, for instance, if my balance is intact and they push me, I'll walk out of the push as a reflection of what I felt done to me.