Dumbing it down

[Essex]

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And while I'm ranting away, just how does Eowyn get 'almost dead?' After racking up an impressive body count, fighting Gothmog (2nd in command?), she kills the WK (and if that weren't enough), runs from the Gimp, and then...what are we to assume? She looks well enough when she chats with Theoden.

It's called adrenaline, and then shock. Just like the unsung hero Merry who was walking around unnoticed after he helped defeat the Witch King in the book, his wounds did not take their perilous hold until later. This has been transposed from Merry to Eoywn for the movie, as she was the one at Theoden's side for his death speech (because film wise the story could not fit a Merry/theoden bonding session in - but this is a pity).

Did Merry break the spell that knit the WK sinews together, or did he sting the WK, bringing him to his knees and causing him to 'freeze' so that (1) Eowyn could have time to say her line and (2) she could stab him in the face easily without the need of a step stool?

Yes, just as in the book (except she said the line before hand), Merry brought down the WK enabling her to kill the WK with a sword to his 'face'. If non book readers don't understand, and book reading cynics can't except it, then too bad.