Separate antenna for radio transmitter and receiver
No, you can't listen and talk at the same time. Ham radio is not like using a telephone. The input of the receiver can't handle the power output of the transmitter.

If you have separate receiver and transmitter units, you'll need separate antennas, or some means of switching one antenna between the two units. If you have a transceiver, this mechanism is already built into the equipment.

"Some means of switching" could be as simple as a manually-operated switch or relay, but more commonly, you have a control signal from the transmitter that's driven by the PTT (push-to-talk) button that operates a relay automatically.