Yes, you are absolutely correct that you shouldn't run SQL profiler on Remote server for long time. That's why I referred you server -side trace where you choose only events and filters you are looking for. We leave Auto_create and Auto_update statistics on all production server as it lets when to create stats and update stats . It is absolutely wrong that it locks table. I think you are talking about Rebuilding index.

Here is the main point:

1) When you are rebuilding Clustered  with DBCC DBREINDEX or ALter index...rebuild, it locks table as it has to drop index and recreate with new clustered index matching clustered key.It updates statistics also with full scan

2) But when you are REORGANIZING index , it doesn't lock table and it doesn't update stats

3)In  SQL 2005, instead of runing  Perfmon or Profiler, you can see status of server and Performance of query with  Standard reports that comes with SQL Server.