Ground is mutual.
I hope you mean Nano TX1 to Mega RX1 and Nano RX0 to Mega TX1.
I have tried both variants. If I join Nano TX1 + Mega TX1 and Nano RX0 + Mega RX1 both arduinos are working (i can see blinking LEDs)
When I join Nano TX1 to Mega RX1 and Nano RX0 to Mega TX1 then Mega freeze.
What are you using, on the Nano, to make data available on the Mega?
Nano is powered from Mega
You need to explain how and why.
I have situation when i need only one USB cable connect with PC - cable from Mega. Mega is powered not from USB but from power source. Nano is not connected to the PC but with Mega.
But I have tried both variants ... both arduinos connected via USB to PC but with the same results = no communication.
(I have not yet tried the examples from Robin2 suggestion.)