I am a PhD student seeking to collarborate with PhD student/professors from other department. How can I make this happen?
Yes, go for it.  It sounds like a great idea.
Regarding your formal status with the other labs you collaborate with, as a grad student you could be considered more appropriately as an &quot;intern&quot; for them, which is not in the usual sense of the word, in terms of responsibilities, but I've seen the term used a lot in academia for researchers collaborating at other labs.