You need to use derived column transformation and with help of expressions perform required conversion operation on original columns.
To replace null with default value use
REPLACENULL(expression 1,expression 2) in derived column transformation.
REPLACENULL returns the value of second expression parameter if the value of first expression parameter is NULL; otherwise, returns the value of first expression.
(DT_DBTIMESTAMP) (ISNULL(SHIPPED_DATE) ? “1900-01-01” : SHIPPED_DATE)
ISNULL([SHIPPED_DATE]) ? "UnknownDate" : [SHIPPED_DATE]
To deal with date part, you can use Concatenate and make into valid date-time format.
Say you have 01/07/2014 as original field value then make it to "01/07/2014 00:00:00"
OracleDateField + "00:00:00"
If you have to perform both operations at same time(checking nulls and dealing with date part ) then it's good to use script component rather than derived column transformation.