Hi Ram,
Create a prompt to select the start and end date. Hope you have already done that
Create chart with date dimension, as you are filtering data for the user given inputs, if you create a graph it will show the data for dates which are in the user selection range.So your 1st requirement will be done with this.
2nd requirement, create a variable using todate(Userresponse("start Date");INPUT_DATE_TIME)
todate(Userresponse("End Date");INPUT_DATE_TIME)
The input to the userresponse function are the prompt text which you used to filter the date values
ex: Date between "start date:" and "end date"