How to receive stream of bytes using PIC USART

[dhouston]

The SpO2 module I use is of none parity.

That's not the issue. How many STOP bits is the issue. If, as the only reference I could find for the BCI protocol says, it uses 8N2, you cannot handle it - all of the PBP methods require 1 stop bit. Two stop bits could explain the erratic results. You need to provide a link to the datasheet for the specific SP02 device you are using.