I can't answer your questions about Indian training requirements, but I can clear up the questions about the US type certificates and what models are on what TC.
The Cessna 172RG is on FAA type certificate 3A17, which also includes the Cessna 175. The Cessna 172R and 172S are on TC 3A12 along with most of the other 172 variants.
The FR172J and FR172K are on TC A18EU, and the F172M is on TC A4EU. Both of these TCs were transferred to Cessna from Reims, and the US is now the state of design for those TCs. There are no models with a "175" in them on either of those TCs.
Tracking down and viewing US type certificate data sheets is relatively easy. Go to rgl.faa.gov, and select "type certificate data sheets" at the bottom of the databases list. You can then search by model, holder, TC number, and a few other options. Here's a link:
https://rgl.faa.gov/Regulatory_and_G...e?OpenFrameset