Which address to state as my own at top of publication? i am a MSc Computer Science student writing on a Work-in-Progress publication for ACM SIGCHI.

This format including PDF drafts is defined here:
(http://chi2015.acm.org/authors/works-in-progress/)!

At the beginning of the paper the address for each author is defined separately. Both my mentor (PhD student) and his Professor have their institute address standing under their names, both the same address (institute at our Uni for electrical engineering). Me and my fellow student are studying at the institute for computer science, i.e. another faculty with significant another address and we are not working nor having an office/address there.

What address should be stated under our names? 

I think we need an address, under which letters arrive us, which I think is not the case for the electrical engineering faculty nor the computer science faculty of our Uni. Do you think so, too?

Consequently, I think our personal home addresses have to be stated. But then it appears strange or unprofessional, because it looks like we are not affiliated with anyone.

What would you think?

Thanks in advance!
Many templates include a place for authors to put street addresses, but they aren't necessarily strictly required. 

In your case, if you look at last year's CHI proceedings you can see that plenty of papers omit it.

For your submission, communication related to your submission will be via email, not snail mail. You can either omit the address entirely, or put the address of your computer science department, it doesn't really matter much. (In the general case, I think it's likely that if a publisher does want to communicate by snail mail, they will ask for the preferred mailing address in the paper submission process, not read it off the submission.)