hi akshay iam from electrical dept. and recently i completed that 

1.if you are good in coding and other IT related staff yes you can have a bright future in IT filed and yes they will allow you

2.according to mine eee is very hardest branch in engineering and if you are good in physics subject it will be ok otherwise we cant manage it at all 

3.opportunities in eee are good if and only if you get good gate score(>700) if you want to settle in electrical field gate is the one and only best option .

mostly they wont allow EEE students even if there much requirement, because there is no scope for EEE students in IT companies , some times they allow EEE students in security fields , if you are good in lannguages then you might get a chance to place in IT companies