Languages

You can get the course deatails from the below given link:
http://www.fergusson.edu/departments/department/id/16
Hope this helps.

Yes, you can but it depends on the college which is offering that option.

For TUM, GATE score should be high enough. But writing only GATE is not enough, you have to write GRE tougher and trickier than GATE to study abroad.

It hardly matters how well you speak English. Universities in Bangalore take admission on the basis of marks and ranks. Even if your English is weak, you will improve with time. Also, there is not such quota for Delhi students. You will come under the category of a non-Karnataka resident.