The second example you gave is not technically correct. A few examples:
את מה היא מסדרת? - What is she tidying up?
היא מסדרת את החדר. - She's tidying up the room.
So, מה replaces חדר (or whatever direct object) in the question.
The verb demands use of את to mark its direct object, so it's still there in the question. Not all verbs do, but לסדר does.
I should point, out as a non native speaker, that I've certainly heard plenty of times where I would expect the use of את with a certain verb, and it's left out. Real language is ever evolving.
oh... I guess I did leave out the part that using 'את' is only with a direct object that is "definite", i.e. with the. If you were tidying up "a" room, you DEFINITELY would not ever use את.
Definitely take what I say with a grain of salt, I I still only have a partial picture of the language.
Thanks @NaftasliFri1 for the clarification and pointing out that Elana's distinction does actually make sense.
The אֶת before מַה is always optional, but maybe its use would trigger an answer consisting of a definite noun: Compare מָה אַתָּה בּוֹנֶה? אֲנִי בּוֹנֶה גְשָׁרִים What do you build? I build bridges (generally) with אֶת מָה אַתַּה בּוֹנֶה? אֲנִי בּוֹנֶה גֶּ֫שֶׁם שַׁ֫עַר־הַזָּהָב בְּסַן פְרַנְסִ֫יסְקוֹ What are you building? I am building the Golden Gate Bridge in San Francisco (just now specifically). But this usage is propable quite fuzzy.
According to an earlier example I answered "What is she organizing for?" and suddenly NOW the 'for' preposition at the end of the translation is not correct. Let's be consistent. My earlier impulse would have been to translate 'For what is she organizing?", but because of the earlier example which I got wrong the first time now the 'for' is not acceptable? Does not make sense and is not consistent with earlier example.