Arduino Mega with double 7 segment display

I think you should go for the ~500R series resistors and the pins you suggested. This should keep it under 165mA in total. The two grounds thing is probably irrelavent because they will be connected together on the Mega's pcb anyway, but go ahead with it if you feel safer.

However, you need to avoid using the pins that your ethernet shield uses. You didn't say exactly which type of ethernet shield you have. The current version of the standard shield says:

Arduino communicates with both the W5100 and SD card using the SPI bus (through the ICSP header). This is on digital pins 10, 11, 12, and 13 on the Uno and pins 50, 51, and 52 on the Mega. On both boards, pin 10 is used to select the W5100 and pin 4 for the SD card. These pins cannot be used for general I/O. On the Mega, the hardware SS pin, 53, is not used to select either the W5100 or the SD card, but it must be kept as an output or the SPI interface won't work.

So you should not use pins 50 to 53, 4 or 10 for your display segments.