1999 Pontiac grand am horn goes off by itself and locks are locking and unlocking by themselves

How are you 'locking it' to make the noise?

clock spring connection and is a known issue.

https://www.google.com/search?q=2004+pontiac+grand+am+horn+not+working

What does 'cruise control' have to do with the horn not working?

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Horn goes off when ? Vehicle just sitting , going down the road ? Same with locks ? If when going down the road , could have a bad door ajar switch ! Is there a light of a picture of a car with door open lit on the instrument cluster ? Door Locks Go Crazy 1

check wiring to switch sounds like a ground out

IT is probably just letting you know that it has received the lock signal and has secured the vehicle. Horn beps or clearence lights flask

replace the horn itself located in front of the radiator, that took care of my ame problem 7 years ago

No disconnecting the battery won't reset the transmitters. Make sure the battery is correct and installed properly. Hold the lock and unlock buttons together for 7 - 10 seconds, the horn should chirp 3 times when its good. If this doesn't occur then the transmitter is faulty.

Hold down the the lock and unlock buttons on the remote while by the vehicle for about 10 seconds this should reset the key fob.The locks may cycle but should correct the issue.

https://s1.postimg.org/y2530m1an/door_locks.jpg

Click on the link. I tried to get everything on one page, which makes it harder to read. It's been my experience that posting multiple images, only the first image posts, not the others. I didn't see a relay in diagram.
The bcm controls door locks with input from the door lock/unlock switch, I doubt I can trouble shoot that from here. You could check for bcm trouble codes, see if anything comes up? Some of the national brand auto stores will check po codes for free, I don't know about bcm codes?
Could be other issues.

Possible the system is deactivated.
1. Sit in the driver seat, turn the key on.
2. Hit the unlock doors button 3 time (within 5 sec of each other).
3. Turn the key off and hit the unlock 3 times again.
You should get a chirp from the horn.
If this does not solve your problem, you can try the same proceedure but hit the Lock button Vs the unlock button

sounds like your bcm is internally malfunctioning