One of my close friends graduated from NIT Raipur Metallurgy and did not find the branch worth the money he spent. The placement opportunities were rare and no exposure was offered. Most of his batchmates had to go for non-core options because only that would pay them well. Another major issue is that there are no coaching classes available in Metallurgy for GATE. The workload is considerably less than other branches. There are a few professors with excellent profiles like Neha Gupta who will assist you in genuine research work.
Honestly, I dont see a promising future in the field of Metallurgy so I will suggest you go for other options for branch change like Chemical and IT. Their placement scenarios are very promising and they are likely to be the next big thing after CS. In chemical, the GATE, and college placements have better vacancies while IT will help you in this world of Artificial intelligence.
Coming to the next part of your question, regarding MTech in IITs, I will suggest you only choose between IIT Bombay. Moreover, your chances of getting selected for a PSU increase through GATE in comparison to core branches because the competitors are plenty.