JEE Main

No, these marks and the specifically the rank you have can be used once in counseling of 2019 admission.

Actually, every student take drop to prepare for JEE Mains. Many student go Koto for best coaching in India to be a part of IIT by cracking JEE Mains exam. All what you need to find if you have potential to crack the exam at once. If you can then there's no need to take drop for JEE Mains preparation.

Prepare on your own. Don't rely on any coaching institute, instead get a good internet connection and start studying online. This will be the best way to study and get the most out of your time. What you need is to focus your class 12th books Basics. NCERT textbooks are the best for IIT preparation. Just go through the books very thoroughly and then finally give lots of mock tests etc. To get a nice practice.

JEE Mains and board exam preparations can be done simultaneously, but it will be a bit tough. Get your basic concepts right. Follow NCERT textbooks and revise regularly. After class 12th, it shouldn't be too hard. The questions in JEE Mains is purely based on NCERT. You may enrol into a coaching centre to learn shortcuts and time-saving tricks which are generally not mentioned in the books.

https://www.shiksha.com/college-predictor
Here is the link.

Predict the college according to your rank/percentile. https://www.shiksha.com/college-predictor

Check what colleges you can get into, use the link below:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993

You can check the link for college predictor. Also, if you are thinking about NIT Srinagar, then you've good chances to get in there with your rank for both EE and ECE. So, try your luck. You have fair chances.

Write the exam but you can not attend the counselling for NITs which are the most reputed colleges in country after IITs. So, you can either go for improvement of 12th along with the JEE preparation.