Single Phase Watt Meter using MSP430AFE2xx

Yusuf Aslan said:

. Is a current transformer required always or is it possible to use only a shunt resistor on the current channels?

It depends on your application.

The MSP and its ADCs work relative to GND. However, input voltage of MSP is also limited to a few V above this GND level. Using a shunt resistor means you are connecting the voltage level of the shunt with the GND level of the MSP. Depending on connection, the MSP is now hovering on AC voltage level. This might be dangerous if touching it. Also, connecting the MSP to the debugger will instantly fry the MSP, the FET and maybe the PC.

Using a current transformer makes the MSP side of the metering application independent of the power line voltage level. For multi-phase metering, using transformers is a must. For single-phase metering, it depends on your application - and your coding skills, as you cannot use a debugger or require an insulating USB connection.
You still need a shunt, but on the second side of the current transformer. Since the current transformer usually has a transformation level below 1:1 (100:1 or 10:1), the secondary side current is much smaller and the power dissipated on the shunt is even smaller too.
(imagine a shunt where you have 0.5Veff @ 10A, this means the shunt emits 5W of heat - with a 10:1 transformer, the current through the shunt is only 1A = 0.5W)

Yusuf Aslan said:

Which parameter in the source code "AFE_EVM" should I modify with respect to my current sensing device? 

No idea. But you should be able to figure it out yourself. Once you understood how the firmware is working, you also know how to change it. And you should know what you're doing in any case - if it is  a commercial application, you should develop your own firmware and therefor know what it does, and for a hobby project, you should also know what it does or else buy a commercial device (faster, cheaper, same learning effect).