The hand brake light if I remember correctly is also used to indicate low brake fluid in the master cylinder reservoir. So check the levels and top up if needed. The door switches get dirty with time, pull them out and give them a clean and this will most likely fix that up. The seat belt light only comes on for a short amount of time and goes off unlike the newer cars where a chime annoys the hell out of you. Are you just trying to lock the car with the key in the ignition? Or are you talking about locking the doors for safety while the car is being driven? I dont think the car can be locked with the remote while the key is in the ignition as a precaution so that keys dont become locked inside the car. But you should be able to lock the doors from the rocker switch on the drivers door while inside the car with the keys in the ignition.