Thank you for your reply!
avr_fred:
This makes no sense. Either you still have a chip in the Uno board (which you cannot have when using it as a serial converter only) or you haven't shown a correct schematic when testing as there is no physical connection shown between the at328 on the breadboard and the USB connection.
Let me clarify: My set-up is as shown in the drawing (no connections between the RX/TX lines of UNO and at328 on BB). The problem identifies only using the oscilloscope in that case (since I don't have a separate TTL2USB conveter just yet).
What I mean by "using the UNO's TTL2RS232 converter" is that it's an additional way I can identify the same problem. In that case, I would always either put a wire between the UNO's RESET and GND or take out its own at328 as you suggested. Without delay, this works, and shows the output on serial monitor. With delay, it doesn't.
Let me know if there's more cases which I haven't clearly pointed out. 