Zed

My wife's 2000 CR-V SE has just developed the following problems:

1. The dome light stays on all the time unless the switch is in the off
position.

2. The power door locks will not lock with the keyless remote or the switch
on the door panel. All four doors will lock by pushing down on the plunger
on the driver's door. However, the keyless remote and door panel switch will
unlock the doors. The keyless remote will also pop the tailgate glass.

3. The key reminder beeper starts to sound when the ignition is shut off and
the door is still closed. It goes off when the ignition key is removed.

Does anyone have an idea of what the problem could be? Thanks in advance for
your assistance.