As has already been mentioned, the TSA will cut off locks if they need to search your bag, so locking it is only a hassle to them.
As far as "all bags are screened", yes, this is true, but the screening varies by airport, and sometimes even within the same airport. (and here the government told us that the TSA was being created to standardize airline screening)
Some airports will screen your bags using what is known as an ETD (Explosives Trace Detection) swab before you're even allowed to go to the check in counter. Other airports will run the ETD swab out of sight of the passengers. Some airports will put bags through a large x-ray machine in front of the passengers, others will do it out of sight.
As far as having the bag opened and searched, that happens routinely, sometimes just randomly, sometimes every 50th bag is opened, etc. Your bag is also a lot more likely to be searched if it triggers the ETD, or if they notice anything suspicious on the x-ray. Apparently, the contents of some shampoo bottles can appear similar to explosive matter on some xray machines, which is why a seemingly innocent bag may be more likely to be searched.
The "Travel Safety/Security" section of the Flyertalk.com message boards has a lot more information about baggage screening, if you're still interested.