JEE

Some of universities like IPU and some others conduct lateral entry exams for second year while you can take admission this year and again appear for entrance exams.

Yes, you will definitely get BIT-Mesra with 128 marks.
Also, your class 12th percentage is more than 75%, so no issues at all.
Just wait for the JoSAA counseling 2017.

Following are the top colleges for engineering in India:
IIT
NIT
GFTI
State government colleges like DTU, NSIT, IIITD in Delhi and other government colleges in state. You can easily get admission in your state NIT with 106 marks in JEE.

You are eligible to take admission in your state’s NIT. Also, you may get admission in other government colleges of your state. So, just wait for the JoSAA counselling.

Sorry to say but you haven’t cleared JEE Mains required cutoff. So there is no way to get a good college with your score. You may get admission in any private college on the basis of 12th score.

Yes, you have fair chances of getting admission in MNIT, Allahabad as you stay in UP. So, your home state quota will work fine along with your OBC category.

Sorry to say but you haven't cleared JEE Mains required cutoff. So, there is no way to get the best college for CSE. You may get admission in any private college on the basis of 12th percentage.

Sorry to say but you haven't cleared JEE Mains required cutoff. So, there is no way to get the best college for mechanical. You may get admission in any private college on the basis of 12th percentage.

Sorry to say but you haven't cleared JEE Mains required cutoff. So, there is no way to get the best college for IT.
You may get admission in any private college on the basis of 12th percentage.

I'd suggest against taking up engineering if you're not sure of what you want to do, because it's a rat race out there, and you'll regret it later. I'd suggest you choose between the other two.