Here are several examples of serial in and out.
http://www.melabs.com/resources/samples/pbp/ser2mod.bas

Now for the
What should I do to avoid the data from crashing in Rx buffer of PIC UART, provided I cannot control over the stream of bytes received?
You are using software for serial so the only time anything gets into the PIC is when you ask for it. If you were using hardware then the buffers would need to be cleared.

'send byte to PC
SerOut2 PORTB.6,16572,[B0]
Earlier you said the PC was running the port at 9600? Did you change it for the above test to 4800?

And modifiers. The examples on the above link talks about DEC and such VS ASC||. You might need one.