Question 1 ) &E2,C2:C1000 is date field ?

Here's an explanation of the arguments of SUMIF here.

SUMIF(
A2:A1000, -- the dates to be compared with the upper/lower limit
"<="&E2, -- the test: "less than or equal to the upper limit"
C2:C1000 -- the counts summed when the test is met
)

The "&" in the second argument is string concatenation. So if the upper limit in E2 is 31-12-2012 then the test is (in effect)
<= 31-12-2012

Combining the two SUMIFS, the formula says
Start with the sum for dates <= the upper limit.
Then subtract off the sum for dates < the lower limit.
This leaves the sum for dates in between.


Question 2 ) if I wuld like to have a database ( eg. access ) to store
the large data , how to make it ?

Maybe somebody else can respond to this part.