JEE

Yes, you can easily get that. The only thing you have to do is to apply to the college as soon as possible because there is first come first serve basis for the admission.

You won't be able to take admission in that because there is only one college in the main campus of the university that is NIELIT-Aurangabad and it only takes admission via JEE Mains.

If you don't have any specific choice for doing B.Tech then you can get most of the NITs, IIITs and almost all the GFTIs without any problem, but if you wish to do it only in a specific branch then it might be difficult for you to do that.

It is just fake news that you have got and nothing else. Both the institutes are participating in JoSAA 2018, as usual.

Check out the predictors below:
JEE https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
MHTCET https://www.shiksha.com/mhcet-college-predictor

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Use this college predictor link I am sharing to know about which college you can get.
Good luck.

Category OBC-NCL
Qualified 65313
Max Marks 73
Min Marks 45

Yes, you will get the CSE in Apex Group of Institute.
But there are still very good colleges that you can get on your rank and marks basis.
If you are interested to find out the list of colleges that you can get on your rank basis then do click on the given link and watch it till the end.
https://youtu.be/hOlit6Un7l0
https://youtu.be/3YAzEP1vgvQ

No, you can't get BIT Durg. Apart from BIT Durg, you can get many colleges on your rank basis. If you want to know the list of colleges on the basis of your rank. then click on these videos and watch it till the last:
https://youtu.be/3YAzEP1vgvQ
https://youtu.be/hOlit6Un7l0
After watching the video, follow the steps as described in the video.

You can just visit the JEE Advance 2017 key word to visit the Advance 2017 application form.