Exam

Yes, you can prepare from home and can appear for CAT. However, it would be quite difficult for you to get admission in IIMs until you are born genius.

Yes, if you belong to Andhra Pradesh and want to take admission in NIT, there are quite less chances for you to get a seat in any of the remaining branches in last rounds.

Hi Ritik,
To be frank, it would be quite difficult for you to get Computer Engineering in VIT Pune. I would suggest you to think of the regional colleges in your city/state. Also be open for IT or ELEX/E&TC, of interested.
I hope this helps.
All the Best!

I don't know about Maharashtra spot round counselling but in most of the universities, spot round will start in first week of August.

Yes, you will definitely get the here. The last year's closing ranks under general category for KCET in few branches are as under for an assessment:
1. B.E CSE Closing rank 32126
2. B.E ECE Closing rank 64745
3. B.E information Tech Closing rank 41248
4. B.E EEE Tech Closing rank 108399.

Getting a seat is very difficult at this rank. Further, not appearing in practical exam may also a big issue during the counselling and admission process.

Yes, there are a few institutes whose cutoff for 12th is around 50%. Just search for B.Arch colleges in Shiksha home page and choose in which location you would like to stay. Based on that, you will get the list of colleges, just check their eligibility and apply.

It is not possible for you to get admission in any of the top B.Arch colleges.

Dear Shivani,
Check the below link to find preparation guide for the entrance exam, syllabus and pattern of the exam. You can also get more insight about the marking scheme and important dates.
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.shiksha.com/college/sant-longowal-institute-of-engineering-and-technology/sliet-set-exam&ved=2ahUKEwiD9uLes8riAhUBbn0KHcd0CvEQFjAFegQIAhAB&usg=AOvVaw2nm35y2sKde-FUuodlwndK&cshid=1559464995857.

It is better to wait for the rank. Until the rank come it is very hard to guess. Once the rank come it will be very easy to guess whether you will get it or not.