Hi @Mo_Islam ,
Q1:
Do you mean that your filter function only works when you select 2 Jun to 7 Jul, but not work when you choose 2 Jun to 9 Jun?
Try this formula:
Filter(Test_Rabat,
DateValue(Text('Start Time',ShortDate)) >=DatePickerFrom.SelectedDate,
DateValue(Text('Start Time',ShortDate)) <=DatePickerTo.SelectedDate,
DateValue(Text('End Time',ShortDate)) <=DatePickerFrom.SelectedDate,
DateValue(Text('End Time',ShortDate)) <=DatePickerTo.SelectedDate
)
If the problem still exists, could you tell me how many records are in your data source?
If it it smaller than 2000, you just need to change the delegation limit to 2000:

If your data source has more then 2000 records, then you need to figure out delegation problem.
Since "<>" does not delegate for sharepoint, so in your issue, I suggest you use collection to avoid delegation problem.
The solution is: save your data to collection, then filter that collection.
Q2:
Could you tell me how many days do you want to scroll by clicking the red icons?
I assume that :
if you click "<", selected date of DatePickerFrom will scroll back one week.
if you click ">", selected date of DatePickerTo will scroll front one week.
If so, try this:
set the "<" button's OnSelect:
Set(fromdate,DateAdd(DatePickerFrom.SelectedDate,-7,Days));Reset(DatePickerFrom)
set DatePickerFrom's DefaultDate:
If(IsBlank(fromdate),Today(),fromdate)
set the ">" button's OnSelect:
Set(todate,DateAdd(DatePickerTo.SelectedDate,7,Days));Reset(DatePickerTo)
set DatePickerTo's DefaultDate:
If(IsBlank(todate),Today(),todate)
Then if you click the "<" button, selected date in fromdatepicker will scroll back one week.
If you click the ">" button, selected date in todatepicker will scroll front one week.
Best regards,