Can you do Serial between Arduino Uno and two devices (PC + 2nd Ard)?

I want to achieve Serial communication like this:

PC <—> Arduino-Uno#1 <—> Arduino-Uno#2

In other words, I want Arduino1 to be able to speak (both transmit + receive) with both Arduino2 and PC at the same time.

Is it as simple as connecting Pins 0->1 and 1->0 between Arduino2 and Arduino1, and leaving the USB connection to PC as it is? Or will I damage something if I have two Serial devices trying to communicate on the same port?

You can stay on serial for the monitor in the usual manner, and use software serial to communicate with another device.

You probably won't damage anything, but it won't work. Use the hardware serial (pins 0 and 1) on Uno #1 to communicate with the PC. Use a software serial port on Uno #1 to communicate with Uno #2. Uno #2 can connect with hardware serial or sofftware serial. I would use software serial on Uno #2 and keep the hardware serial (USB) on #2 for code upload and debug. There are several sofftware serial libraries. Choose the one that best meets your needs.