The DDL and some sample data of the type of duplicates you want to move would be helpful.

I've found performance to be the biggest problem with a MERGE. If you can replace a merge with an update followed by an insert it will give about 60% better...

I hadn't read the information about the source table being on another database. A good way to go is to first copy the data onto a Staging table...

;WITH Data AS
(
    SELECT * FROM (VALUES
        (1, 1, 'Begin', CONVERT(datetime2,'9/29/2019 9:00:05.656 AM')),
    ...

This would...

I don't...

Can you wrap the entire job in a TRY CATCH blocks?

In the try block begin and commit the transaction

In the catch block rollback and re-throw the error.

SQL Server caches the execution plan of queries, it may recompile a query a different way if it is executed at different times.

If there is any difference in the text...

CREATE VIEW [dbo].[vwstudent]
AS
SELECT STD.ID,
       STD.StudentId, 
       CASE WHEN STD.EfDate <= c.value THEN DATEADD(MONTH, -2, STD.EfDate)
...

That seems a very odd requirement. Are you sure your users really know what they want?

If you are using SQL 2008 you can't use LEAD and LAG. I think you might be able to use the windowed SUM function though.

;WITH Data AS
(
...

CREATE PROCEDURE #TestDW 
(
    @CheckDayOfWeek bit = 0
) AS
IF @CheckDayOfWeek = 0 OR DATEPART(dw,GETDATE()) IN (3,6) BEGIN
    PRINT 'Hello'
  ...

UPDATE a
   SET a.invalid = 1
  FROM aaaMyTable a
 WHERE EXISTS(SELECT * 
           ...

After rebuilding a clustered index you might also need to rebuild all the non-clustered...

This is equivalent SQL to yours, but instead of checking the left join column in the WHERE to be NULL or equal to something else, you might as well check...