1. I have a wall switch (WS12A) controlling a ceiling fixture. Of late, the fixture doesn't seem to turn off at all. I have tried the switch, remotes etc and nothing works. The only way to turn it off is turn off the "mini switch" at the bottom of the switch
You most likely have a noise source and/or a signal sucker on the same electrical circuit as the light. You didn't state it, but I'm guessing you can turn the light on just not off. Your signal is probably borderline and when the light is on, it's not strong enough to turn it off.
2. I have a couple of other lights - a chandelier among them - that will turn on with a remote but won't turn off unless I press the wall switch
Same as above.
3. I have 2 floor lamps that are connected to 2 appliance modules with the same code. I can turn both on and off with a remote. I have a motion sensor that is supposed to turn these on but only one of them turns on. It seems like the one closer to the motion sensor doesn't turn on. Is there a certain minimum distance between the sensor and the module that is needed
The physical distance of the motion sensor to the appliance modules is irrelevant.
The physical distance of the motion sensor to your transceiver is. Since one of the appliance modules turn on, this is not your problem.
The electrical distance from the transceiver to the appliance modules is more likely the issue here. However, you state that they both work with a remote and only one works with the motion sensor. Do you have more than one transceiver in your set up?
I think most of your problems are from signal degradation. The best advice is to
MAP / MEASURE / CORRECT. If this set up was working for you before and then suddenly stopped, look for some new electrical device that was recently plugged in.