Wireless Communication with NRF24L01+
firstly, the radio.write command is used for checking for the acknowledgement from the RX after the FIFOs are full for a single write. But radio.writefast will not wait for the acknowledgement from the RX and would continuously transmit the payload for a single write. Similarly for radio.startwrite and 
radio.startwritefast commands.

Coming to the keeping the NRF in listening mode, even I haven't tried it before so I cannot suggest an exact solution for this problem. But as far as I know,  you can go for writestart command to keep the reading pipes open while you are sending. But I would personally suggest you to confirm this from datasheet again before experimenting.

For ACK payload, it depends upon the master unit controlling the SPI communication with the NRF chip and thus, by maintaining a mutual understanding between the RX and TX units, you can define the payload for acknowledgement signal as well.

Coming to best speed possibility, To increase speed, NRF has three speeds from which you can select the highest value available. Also see which pipe/channel works the best for you so that you can achieve the least number of lost packets.