No, that doesn't work. "Mi te csinálsz?" is not a valid sentence.
Mi is nominative case, so it would be the subject, like in "Mi folyik?" - "What is going on?" The "what" is doing the thing. But in the original sentence, you are doing the thing to the "what", so in needs to be in accusative case and get a -t suffix.
Okay, good. But I have to point out another thing, then. :´)
"Mit te csinálsz?" still doesn't work. The question word (or phrase) always has to be in focus, i.e. right in front of the verb stem. The only valid word orders you can have here are
- Mit csinálsz? - What are you doing?
- Mit csinálsz te? - What are you doing?
- Te mit csinálsz? - You, what are you doing?
No, "Csinálsz mit?" isn't valid either. The phrase "mit csinálsz" really has to stay like this.
I am also not sure why you want to emphasise the action here. Okay, maybe to contrast it with "What are you cooking?" or so. In any case, you can just vocally emphasise the verb: "Mit csinálsz?"
I didn't exactly know where to ask this so I'll just ask this here: one of the sentences I've come across were the sentences "egy lány van itt" and "a szék mindig itt van". According to my Hungarian mother "a szék mindig van itt" is wrong, but why is "egy lány van itt" correct? What exactly is the rule behind this? I'm sorry if this is explained later on, but I've just been wondering
A szék mindig van itt. is indeed incorrect and Egy lány van itt. is correct
It is because of the word mindig. This word and a few more has a compulsory word order
Mindig itt van.
Néha itt van
Állandóan itt van
Ritkán van itt.
Soha sincs itt.
So, A lány van itt. becomes A lány mindig itt van.
A szék van itt. will be A szék mindig itt van.