"on the rail" means placing the 4700uF capacitor between Vcc and Gnd.
You need two resistors to get 3.3V from 5V Pin17 output.
And its better to use battery for GPRS module.
On a 28X2, HSerin & Hserout are Schmitt Trigger type. Status High if input >0.8 Vcc picaxe. See Input type on picaxe...