Hello Aakash,
Lets attack your questions step by step
* First of all you should not compare placements in terms of salary right now in selection for campus. Nobody knows what salaries are going to be like 4 years down the line. Having said that, a well established institution always has a better chance of prospering than a newly opened institute. In your case, BIT mesra is clearly the choice that stands out.
* Secondly, agreed that Goa is a nice place as compared to Jharkhand. But let's understand that you are going to a campus not a city. Campus life is always secluded from external happenings in the city, though not completely but to a great extent. So, if want to enjoy all the established facilities, proper order, nice faculty, better peer group, BITS mesra is the place to go.
* ECE always has and will always have bright prospects as compared to Mech. You are right in pointing out that many institutions are coming with ECE, but so does are the oppotunities. In this growing electronics, its better to opt for ECE than mech.
Hope this clarifies your query. Please revert back in case of any comments.
Regards,
Ankit Jain - IIT Bombay