Medical Ultrasonography Phased Array Beamforming
ad1) While transmitting the signal could come back, therefore if the object is far ditant it could send a burst then switch to receive, but I think a more stable solution is to have a transmitting array and receiveing array separated.
ad2) It is possible to send a directed cone in spherical coordinate sytem, then to receive the reflected signal. The reflected signal indeed comes with a delay, therefore the possibility to differentiate the timestamp of sent signal is to encode the sent signal with some orthogonal function and then doing the correlation, in few words: you do encode xmit signal with a known function, then when you receive you do the correlation between recived and sent signal, so you get the exact delay (travell) time. Imaging usualy uses those chirp signals that can reject near objects (the transmitter itself) by use of correlation math.