Can we use group by and where condition with same fieldname

You can, but the "GROUP BY" clause is used for grouping together sets of rows, so it does not make sense for your question (or anything that involves a "SELECT *").

To answer your question though:

SELECT DATEADD(dd, 0, DATEDIFF(dd,0,StartDate)) AS 'StartDate', <other fields>
FROM   Employees
WHERE  StartDate BETWEEN '15-Jan-2011' AND '20-Jan-2011'
ORDER BY StartDate

Note: the stripping of the time from the date came from here

Absolutely. It will result in filtering the records on your date range and then grouping it by each day where there is data.

It should be noted that you will only be able to select the startdate and then whatever aggregates you're calculating. Otherwise, it should work perfectly fine.

For example, this query will give you a count of employees for each startdate:

SELECT startdate, count(*)
FROM employees 
WHERE startdate >= '15-jan-2011' 
      AND startdate <= '20-aug-2011'
GROUP BY startdate