Can you also say: "Neden burada oturuyoruz." ?
Yep and this is already accepted.
What is preffered when we talk about living somewhere: oturmak or yaşlımak?
both are equally good , but it is yaşamak not yaşlımak :)
Can I use Burayı instead?
Nope...you are talking about "at which location" you are living and ergo must use the locative.
Does neden have to be the first word?
you can also say 'burada neden yaşıyoruz'
Hello :) I would like to know if we can use burası instead of burada? Why/why not?
no. burası is like "this place", so it would be like "Why are we living this place?" instead of "Why are we living in this place?"
(here means both of those in English)
Burada yaşıyoruz neden
Was marked wrong , why?
"Neden biz burası yaşıyoruz" why it is wrong?