Mr. Tines: Still unanswered, how they caged the raving beast; and what state it was in at the time (e.g. shedding more and more armour)
UrsusArctos: Sadamoto tried to address this in his manga by having Tokyo-3's surviving defensive systems restrain the rampaging Eva, with the implication that the city's defenses were really built to keep the Evas in rather than the Angels out. Not the greatest of explanations, but there doesn't seem to be a better answer to the question.
Mbryo: I'm guessing that Yui let herself be captured, or just shut down on her own after she was done with all the screaming. She did the same thing in Episode 02 and 16. Yui is in control of the Evangelion's actions so despite how animalistic she may appear to be, she has no reason to be hostile towards humanity.
