On a 12F683, GPIO.3 is "Input Only" when not used as MCLR.
You'll need to use a different pin for the LED.

And the receiver has no way to know where each byte of serial data starts.
The sender is continually sending data and the receiver looks for data whenever it looks for it.

If the receiver starts looking in the middle of a byte, it doesn't know it's not the beginning of the transmission and will receive an invalid value.

There needs to be some sort of handshaking, so the sender knows when the receiver will be ready to receive something before sending it.
That will take another line between the two chips.
Or, tri-state signaling on the single line (no sample code available).

My recommendation ... add another line between the two chips, use SEROUT2/IN2 with FlowPin control.
You can use GPIO.3 for the serial input (put FlowPin on another pin).