Sounds like DOMAIN\GroupName is a group and DOMAIN\user.name is a member of that group. This means that DOMAIN\user.name has access to SQL Server through that group. You have 2 options:
Create another group, let's say DOMAIN\NewGroupName and grant that group INSERT and UPDATE, then make DOMAIN\user.name a member of that group.
This is not the fastest ...
how to set the value of @MaxItemSeqNum to the returned result
SET @MaxItemSeqNum = ( SELECT MAX([Table1].[Item_Seq_number])
WHERE Batch_Id = 1
Group By Batch_Id );
SELECT @MaxItemSeqNum = MAX([Table1].[Item_Seq_number])
There are only 2 or 3 rows in sys.dm_exec_requests with status = running
A running SQL Server request will cycle quickly (perhaps every 4ms) between running, runnable, and suspended. running means that the task is actively using a CPU core (aka a Scheduler). runnable means that it need to use a Scheduler, but it's waiting for one to be available, and ...