Engineering

If you want a well-established government college, then it can be little difficult but if you want only "government college tag" then the four newly established government colleges I. e. , Rajkiya Engineering College (Band, Mainpuri, Ambedkar Nagar and Bijnour) are easily obtainable as per your rank

Yes, you have chances to get in.
All the best.

You can get government college. But first choose your destination course which you are want to do. Please visit the link given below for best colleges based upon your JEE rank
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=6919

AMIE is done generally to get an UG degree. It is mostly done by working class students to complete UG for promotions or apply for new jobs. It has very less applications than that.

Hello siddharth
Do not worry if you were unable to qualify JEE. There is vast scope of every field but it depending upon us how much we are giving our best out of best. Today's the aeronautical engineering is growing very faster and has very vast scope and provides a lots of career opportunities. So

B.Tech is best option if lateral admission is taken as it will be of 3 years that way. AMIE gives an equivalent degree in 2 years but its recognition is in doubt and is less preferred among employers.

Not necessarily. AMIE will help you in pursuing higher studies and may be in promotions but it is not given much preference by employers as it is done through open mode and doesn't give a student enough practical knowledge.

Government Polytechnic, Pune is better than Nashik. Pune has good placement records than Nashik. Pune has 2.5 lacs per annum average placement rate whereas Nashik has lower.

Seats for lateral entry depend on the basis of vacant seats in the second year.