You can't feel the zip (there's a lot of padding underneath!)
I just unzip, and kind of push the whole side under my boob, but I'm a C-D cup so maybe if you are smaller it wouldn't work.
The whole singlet is very stretchy/lycra and you can adjust the straps I don't think anyone large would have any trouble if they order the right size.
Because it's under my boob, it's not anywhere near the baby.