Programming a calculator in Delphi

For changing the sign, you simply do

...onclick...
number=number*-1

for the square root it's here http://www.delphibasics.co.uk/RTL.asp?Name=Sqrt

regarding 0
If zero is divided, the result is always 0
if 0 is the divisor, it's an error

either you handle it with a try ... except
this is the case handled here http://www.delphibasics.co.uk/RTL.asp?Name=Except

otherwise simpler:
if divisor=0 then
exit