all punto's with the 1.1 and 1.2 8-valve engines make a funny whining noise when cold - this is caused by the cambelt tensioner and is normal. really loud screeching is most likely to be a slipping fanbelt or power-steering drivebelt - re-tension or replace the offending belt (check for oil contamination too). heat allows the belt to stretch a little and lose tension - so the noise can be eliminated usually by increasing tension. brake noise also plagues puntos, i suffer the same "squeaky brake" on left-handers.
all these little faults are basically down to crap design and build quality - i.e. what fiats are famous for! and yet we still love 'em!
FIAT: Fix It Again Tomorrow...