1999 Chevy S-10 Programming Door Locks

They can be programmed for,
All lock when put in drive, none unlock
All lock when put in drive, drivers side unlocks when shifted to park.
All lock when put in drive, all unlock when shifted to park. (Factory default)
None lock/None unlock

If your locks are locking while just setting still with the trans in park it is a different problem.
If you have a manual trans the factory default is doors lock if vehicle speed is greater than 15 mph and unlock when the key is removed.

Also the vehicle shouldn't lock the doors at all if the drivers or passengers door is open with a key in the ignition unless you manually lock the.

The programming method is as follows.

With key off pull the multifunction stalk toward the wheel. Now turn the key to run and back to off TWICE. Then with the key off release the stalk. The doors should cycle the locks.
You now have 30 seconds to program the locks.

For all lock - drivers unlock you press the lock switch ONCE and then the unlock switch ONCE.
For all lock - all unlock you press lock ONCE and unlock TWICE
For all lock - none unlock press lock ONCE and unlock THREE times,
For NO lock - No unlock press lock TWICE

OK, You have a DEI Valet unit. That can be changed using the jumpers inside the control unit. I have a similar remote start, lock unit in a 95 conversion van.
As for the lights/horn, it depends on how it was wired. Those are user selected options.
Directed Electronics has the owners manuals / installers info online free. But you need to know the model number off the unit. They usually get installed next to the steering column behind the trim panel. The model number will be on a sticker on the controller. The jumpers are under a small cover on the control unit.