Yes it's easy for you to opt for a Masters of Engineering apart from gtu if you are. Doing your bachelors from gtu.

1)If you are getting a proper gate score it's and iisc would be the best alternative.

2) masters of science from any other country to is a splendid opportunity

3)Pursue your masters with gtu through pgcet exam is the last one which I think you don't wanna opt

Yes, you can pursue your M.Tech from any other university as there is no restriction to do B.Tech/B.E and M.Tech/M.E from same college/university. Also, the admission and eligibility criteria varies college/university wise so please share which particular one you are interested in?