yes baby can sleep in a moses basket overnight - our baby is 8 weeks and still sleeps in hers at night.
Mattresses: we were advised by a girl in Murphys baby shop that sprung were better as she said babies would find a soft spot in the foam ones and try and lie in it all the time. have a spring mattress for our cotbed but haven't transfered babs over yet!
best of luck!
Yeah the sprung ones are supposed to be better for them. We had our DD in her moses basket until she was 14 weeks and then she just got too big for it, happy out in her little cot now!