After uploading the code, can I connect a UART peripheral's RX, TX to TX, RX (D0 ,D1) and use the serial monitor of the arduino together ? Will data reception from the peripheral properly work in this case, or will it conflict with the serial monitor ?
You can use the serial monitor in this way, as long as you ensure you do not send anything from the serial monitor out to the Arduino or peripheral, only to monitor data.
That said, if you try to send debug prints from the Arduino to the serial monitor, they will also be sent to the peripheral device, where there may be conflict, depending on the peripheral.
So you technically can, but it's not advised because there are several ways it can go wrong.
One alternative is to use the SoftwareSerial library to create a second, bit-banged serial port. Note, however, that this library can't operate at high speed (probably best to keep at 9600 bps) reliably.