SAT

Applied and Pure Sciences
Architecture and Construction
Business and Management
Computer Science and IT
Creative Arts and Design
Education and Training
Engineering
Health and Medicine

No, you need not appear for SAT exam. An Architecture aspirant should take up NATA exam or JEE Mains paper 2 exams to get admission into Architecture course. Council of Architecture guidelines states: Only candidates who have the following credentials shall be eligible for admission to B.Arch. Course. I. Qualified through the recognised aptitude test in Architecture NATA or equivalent)
ii. Have gone through any of the following curriculum with marks as prescribed below: (a) Secured 50% marks in Physics, Chemistry and Mathematics and also 50% marks in aggregate at
10+2 level examination.

When you are interested studying abroad SAT is a compulsory criteria for it. JEE Mains and SSC are only to study anywhere only in India not abroad. Mostly, SAT is offered every month from October to January.

Hi, Please visit Shiksha.com's college predictor-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor. Ranks keeps on changing every year and differs from one branch to another and one college to another. If you fulfill the eligibility criteria of the specific institute, you may complete further admission formalities. For now, I would suggest you to first contact the institute officials of the shortlisted universities directly for specific eligibility criteria details.