Several bytes have the same timestamp value when I use the TIMESTAMPBYTES with COMM-DRV/NT.

COMM-DRV/NT reads the high performance counters every time an interrupt for character reception occurs. If you are using a UART with a FIFO (16550 UARTs and above), then these UARTs do not fire an interrupt for every character received in a stream in order to increase overall system performance. To solve this problem you should or the flag IGNORE_16550 in the flag parameter of the WCSCVxDOpenPort() or WCSCVxDInitializePort().