Engineering

https://www.shiksha.com/university/Gujarat-university-Ahmedabad-29851
For all the information regarding admission procedure, just follow the link.

https://www.shiksha.com/exams/josaa
Here is the link for all the information.

Yes, it is possible to get admission there by lateral entry.
If you are not form Tamil Nadu then you actually cant apply for Anna university and other universities afillated by Anna with your marks.
You can opt for a management quota where you may have to pay according to the program and the collage you choose in Tamil Nadu.
you can visit their main site for more details
https://www.shiksha.com/university/anna-university-chennai-3084
Thanks.

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Here is the link to get information about your all doubts.

https://www.cucetexam.in/
You can follow the link to get all the official details.

https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Just follow the link to get a prediction of a good college.

Yes, there is chance of getting admission there as there is low cut off for EC.

Dea Raghu Venkat,
No, its really typical to get admission in any branch with such rank in VITEEE. However, to get admission in your desired branch, the cut-off rank will vary considerably.
you needs to get rank under 10K.

It is little difficult to get CSE there, as there is cut-off for CSE is under 10k rank.
Best wishes.

Please visit this link this is college predictor
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.