IIT Kharagpur - Indian Institute of Technology

Aerospace will provide you with more opportunities abroad but ECE will give you loads of opportunities in India itself. Though the thing to consider here is that, IIT Kharagpur is an old IIT & much more established than any of the new IITs which will very much be visible during placements and in other avenues. Please decide accordingly.

I can answer the question for the M.Tech students. In 2015, 2016, 2017 placement sessions, the companies in which the M.Tech candidates got placed are as follows:
Pfizer, Honeywell UOP, Parul University, Cognizant, Lanxess, Aditya Birla Science & Technology, Hikal, EXL Analytics, Tiger Analytics, IOCL RnD, and few more.

It is just fake news that you have got and nothing else. Both the institutes are participating in JoSAA 2018, as usual.

Mentioned college are best on their own place. But, branches are different that you have entered. So, choose branch first which want to pursue. You may go for DTU if you have interest in computer. IIT Kharagpur is also option for you. Metallurgy is also better branch.

See the opening and closing rank you will get your answer. IIT, Indore has achieved 100% placements both in mechanical and computer science and 97% in electrical with a whopping package of 1.7 crores. CS average package is 15.5 lakhs. Indore is better city. It is well connected by airport. Placement get a advantage here. IIT, Indore has better coding culture. It has qualified two times for ACM ICPC. IIT Indore has best overall rank from India for all the ACM ICPCs held till now. IIT Indore has collaboration with CERN, so if you have good grades you get to intern at CERN.

No, you can't not even if you have internationally published and recognized projects. They want GATE. I don't know if it's an IIT thing or an MHRD thing but a person who spends most of his/her day doing really good projects has little time to prepare for exams like GATE and are usually not the type who sit idle and study for an exam for a year after finishing their degree.
So if you're bright, a hard worker, and doing good research/project work, in India you are out of luck.

The admissions are done on the basis of JEE Main rank so to get a rough idea about the college you can get through below link:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.