Horn, Door Locks, and Keyless Entry problems

I have a 1994 Buick Regal Custom, and am having several problems with it. First, on several occasions the horn has gone off by itself; (several times at 2 am...I think it's possessed) sometimes just a brief honk and other times the horn continues to blow until I remove the fuse.
Second, the door locks have unlocked by themselves while I was driving down the road. One time, the horn went off, the door locks started going up and down and the interior light came on and off--all at the same time.
I have also come home to find the door locks "stuttering" on and off (the car is not running, just sitting in the driveway) The locks will go up and down by themselves continuously for up to an hour. The only way I have found to get them to stop is to remove the fuse.
Third, my keyless entry quit working. I have replaced the battery but it still does not work.
Fourth, my antenna quit going up and down like it is supposed to. Up when you start the car and down when you turn the car off, now it just stays up all the time.
Are all these problems related, or is my car falling apart? Please help me!

I've heard of newer regals (97.5 and newer) having this problem, but never a 94. You say the horn stays on, does it pulse(As if the alarm were going off), or one continuous blast?

It has never pulsed like an alarm, once or twice it has been one short blast, but mostly it one long continuous honk.

I still think it has to do with the alarm system, thats the only feature that controls all of the components that are messing up or you.

I don't have an alarm system that I am aware of. Is there some type of system that comes standard with the Buick? Could there be an electrical problem with the car, one that could be easily fixed? I really appreciate that you've taken the time to reply to me, I am grateful for any help!

I had the horn problem with my 1995 Regal. Checked everything determined it was the switch in the airbag/horn assembly. Have no idea how to fix it. I switched my steering wheel for a pontiac steering wheel with airbag. I like the feel of the pontiac wheel a lot better.