If I know for sure the date field does NOT carry any time values then I agree with using the between.  But if it has time, you could miss records. ...

Just added a few tweaks:
DECLARE @StartDate DATE;
DECLARE @EndDate DATE;
DECLARE @PrevYearStart DATE;
DECLARE @PrevYTDEnd DATE;
DECLARE @MonthStart DATE;

SET @StartDate = '01-01-2018';
SET @EndDate =...

Looks like you got the YTD numbers.  Use the DATEADD to determine your Previous year start and end dates, same for month to date.

Start by writing these as...

You have a comma after Facility, that is what is casing the error.

If you are running a DELETE SQL statement you could use the OUTPUT statement to write the rows deleted to another table.
https://msdn.microsoft.com/en-us/library/ms177564.aspx

What part is taking the most time?  Can you split it up to see?
Try replacing the first SQL with something like this:

SET @prep_date_start = COALESCE(@prep_date_start,...

You could try this:
CONVERT(CHAR(11), DateIn, 107) AS DateIn