Can I use arduino USART tx and rx separatly?
RS-232 is really two separate serial lines, one in each direction.  Likewise, UART hardware is independent for receiving and transmitting, except for the baud rate generator.  So as long as you want to use the same baud rate (which you do), there should be no problem.  Think about it.  The micro just sees a RX and TX line.  It has no way of knowing whether they are connected to the RX and TX of one other device, or split so that TX goes to the RX of one device, and RX goes to TX of another.  How would you imagine it could tell the difference?

Of course if the higher level protocols for either of those devices is bi-directional, then this won't work.  If you just want to pass GPS bytes along to your computer, that would work.  However, if the GPS needs to be sent something to get it going or otherwise needs to be controlled, then it won't work.