I have a sketch written in Arduino IDE which monitors on 2 RXs pins signal data and writes it to Serial Monitor. I have a problem that it from 1 RX the data are always written twice, but another RX (response) is OK, what could be the problem?
So I don't think it is problem in program of MCU.
Your SIM800L module may have Command Echo enabled. You can send the following commands to change it:
ATE0 // Disable echo temporarily; After SIM800 reset, saved setting will be used.
ATE1 // Enable echo temporarily; After SIM800 reset, saved value will be used.
ATE0&W // Disable echo and save setting
ATE1&W // Enable echo and save setting
Reference: SIM800_Series_AT_Command_Manual (page 35, page 355 end)