"I want to know is this method of splitting the design ok"

Not just OK. But essential for user safety.

Generally the setup looks fine. Except that you have not made any mention about the MCU power supply and also if the 15V for the proximity is galvanically isolated from this. Maybe you would have done that already.

"8 inches cable in between board and LCD should I use a buffer such as 74HC541 to drive this capacitive cable load. "

Even for 8 inch of cable, would be a good idea to use the buffer .

And on the 110V PCB , hope you have taken care of the minimum PHYSICAL distance between the 110V traces and 15 V traces.

Happy welding.

Raghu