As you probably know the 3-way on diagram A is the second switch and connects to the 3 way on diagram B which in turn goes to the light.

I'm almost certain the to lights you wish to control separately are setup in series which means you cannot control them separately from the wired switches without disconnecting the second light and adding a new wire to one of the switches. Assuming the room is finished this is going to be a pain and expensive.

In terms of the fan turning on and off randomly my first question is whether the fan remote controlled? If so is it possible that something else is on the same channel?

If you really want the two lights to be controlled separately then short of adding the wire the only option I can think to control the lights separately is to hard wire the lights to permanently on. You would then replace the now redundant switches with a wireless remote switch and wireless light/fan control unit (e.g. something like https://www.amazon.com/DEWENWILS-Wireless-Receiver-Lighting-Programmable/dp/B07S2RM95K). I suspect this will be by far the easiest option.

Jonathan

As you probably know the 3-way on diagram A is the second switch and connects to the 3 way on diagram B which in turn goes to the light.

I'm almost certain the to lights you wish to control separately are setup in series which means you cannot control them separately from the wired switches without disconnecting the second light and adding a new wire to one of the switches. Assuming the room is finished this is going to be a pain and expensive.

In terms of the fan turning on and off randomly my first question is whether the fan remote controlled? If so is it possible that something else is on the same channel?

If you really want the two lights to be controlled separately then short of adding the wire the only option I can think to control the lights separately is to hard wire the lights to permanently on. You would then replace the now redundant switches with a wireless remote switch and wireless light/fan control unit (e.g. something like https://www.destinationlighting.com/item/levven-wireless-light-switch-kit/768453?gclid=CjwKCAjwx6WDBhBQEiwA_dP8raoGkiSgl44ImgaMoq3v0wqaHLiEuyKXy0MdGhjzMJZmtpFYdmw1DhoCqDIQAvD_BwE#home). I suspect this will be by far the easiest option.

Jonathan