Why is it not 'make me what you want'?
make me == תעשו אותי
תעשו אותי שמח.
עשה לי את היום
"make me" in the sense of "make for me" -- would that really be תעשו אותי?
Why not משאתם?
If you ask whether you can combine "מה" and "שאתם" into one word, then no - this word doesn't exist in Hebrew.
Those words are said together so commonly that I thought they might be conjoined. Thank you.
You may have confused them with the indefinite pronouns like מַ֫שֶּׁהוּ.
asu is passed and translated in the present.
In the past ("they did") you would usually use the pronoun הֵם.
It's actually also imperative, and this is how it's used here.