Does "čekáte" not need the particle "na" here because there's no direct object?
Not sure but this is how I understood it:
čekat = to wait
čekat na = to wait for
kitbogan Yes, but not always. It is also possible to say:
Čekám (očekávám) dopis. I'm waiting for a letter.
Čekám dítě. I am pregnant.
Čekám tě v pět. I'm waiting for you at five o'clock.
But i think that might better be translated as "await" instead of "wait for". Then the grammar is similar again
I tend to agree.
But it would also work "Proč čekáš?" or am I wrong in my language?
Yes, of course, and it's accepted.