I am working on integrating a web application with ICM and trying to use GED-145 for the same. Is this the same as the protocol being used by MR PG? Can I make use of GED-145 for communicating to MR PG?

Yes, it can be done using this Application Gateway Interface which is a process instance in Call Router. But, it needs an extension called Gateway Host which is a purchasable component from Cisco advanced services who can be reached through custom-application-request@cisco.com.

To be precise this extension component is the one which will enable you to connect Cisco ICM call routing script with a Web Application.

Can we integrate an MR PG using this GED-145 based App Gateway?

MR PG will be configured to interact with call router which in turn can use the App Gateway and then external web App using GED 145.