SQL & PL/SQL :: Convert Varchar2 To Date Or Number

I created table Contains then following columns

cheq varchar2(50)
date_due varchar2(50)

and data entry in this columns

cheq 500,1500,5000 all values numbers in this columns

date_due 1-1-2012 , 15-9-2010 all values in this columns date

i want sum the column "cheq"

when used this code but it's not working

select sum(to_number(cheq))
from table_name but the code not working

second column "date_due"

i want search between to date i used this code but also not working

select cloumn1,cloum2
from table_name
where to_char(date_due,'dd-mm-yyyy')
between to_char(date_due,'dd-mm-yyyy') and
(date_due,'dd-mm-yyyy')

but not work