CBSE 12th

No, you will have to take admission on the basis of merit list.

For engineering maths is compulsory, otherwise you are not eligible for engineering. As in engineering you have to study mathematics in the whole degree of B.Tech. That's why mathematics is required.

Which course are you asking about?

Yes, surely, it will help you.

Since you have completed your schooling from a different state, you will have to submit a domicile certificate for WBJEE.

In order to clear IIT-JEE all concepts should be clear and for that you need to study 11th and 12th thoroughly. 11th forms the basics for 12th, so if you want to prepare for IITs start with the 11th syllabus, you can also take IIT coaching if you face some difficulty.

Dear Saurabh,
You are most welcome in UGI and if you want to get in through UPSEE then you can jot in your preferences while counselling process or you can directly fill in your details at united.ac.in in admission 2018-19 section and secure your seat.

Yes, surely you can get admission with your duplicate TC and it's completely valid.

Institutes like Aakash, FIITJEE help students like you and me who prepare for JEE, they charge you according to your marks obtained in admission test, the better you do less they charge or else better you join IIT programme in your college they may take 5000/-for your books or else you can even get them on internet free of cost.

Yes, you can.
Visit this link to check B.Arch colleges based upon your rank:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=6919840
Visit this link for various colleges which provides you with the brochure:
https://www.shiksha.com/architecture-planning/colleges/b-arch-colleges-india