you shouldn't shrink Production server just to get data to test server. Do you need everything from Prod server to be in Test server?

You can run sp_who2 active .

Looks like memory issues. Which edition and SP level is it? What else do you see in app log?

Try setting up security with sql login on both server.

You have to restart service to take effect.

If you are in SQL 2005, You can take advantage of table partitioning but only in Enterprise edition.