Dear Aklie, http://www.marthomachurch.com/
is a Marthomite website. It has a lot of nice information about their history, liturgies, sacraments, etc. It should keep you busy for a little bit.
The MISC recognises just about everyone, although only the Protestants recognise them. It could be possible, however, that they are recognised by the Indian division of the Assyrian Church of the East (that group often known as being Nestorian).
The patriarchal faction theoretically does not recognise the Marthomites nor the MISC, but their willingness to allow the MISC Metropolitan to celebrate the sacraments in his churches while not even being willing to give our Catholicos the time of day says volumes to me. I'm not sure the patriarch would recognise the Marthomites, and I'm not sure they'd be too interested in him either.