JEE Main

You can apply for JEE Advance AAT paper. And, the application process might start from second week of June. Coming to the date of exam, it might be in Third week on June as there is no official news.

We can't say before any announcement of cutoff marks. However, you can check your chance of getting a college here. https://www.shiksha.com/b-tech/resources/jee-main-rank-predictor.

You have a quite less chance of getting an NIT.
You should reappear in JEE Main exam so that you can improve your score.

NTA score and percentile are the same thing.
Your approximate rank will between INR. 6000 to INR. 8000.

Your rank will be around INR. 8 k -10k, so from home state quota you will definitely get it, because last year rank in HS reach 11k and if you are from other state. Well, make a try, but chances are very less. And, one more thing it is MANIT, Bhopal not MNIT. MNIT is in Allahabad.

The final AIR will be declared after April 2019, considering the best score out of the two JEE Main attempts for all the applicants. Hence, based on current percentile we cannot predict whether you can get admission or not. Wait for the final AIR declaration.
Details:
https://www.shiksha.com/b-tech/articles/how-to-calculate-jee-main-rank-from-percentile-blogId-19953

Check out the predictor below for MHT CET and fill COEP in select preferred college's option:
https://www.shiksha.com/b-tech/resources/mhcet-college-predictor
For JEE:
The final AIR will be declared after April 2019 considering the best score out of the two JEE Main attempts for all the applicants, hence based on current percentile we cannot predict whether you will qualify or not. Wait for the final AIR declaration
Details:
https://www.shiksha.com/b-tech/articles/how-to-calculate-jee-main-rank-from-percentile-blogId-19953.

If you want admission in NITs, then your rank should be less than 20,000 i.e 175 marks in JEE Main and 93% in CBSE boards.

JEE Advance is qualifying exams for IITs. And, JEE Main exam is for NITS, IITs and CFTIS.