SAT

Hi,
Ivy Leagues are quite competitive as you might know. They not only prefer students with good academics but also students who have a well-developed portfolio. In addition to excelling in academics, you must have solid extracurriculars, state or national level projects, sports, writing, music whatever is of your interest so that universities know you have a solid profile and won't go wasted. You can target a score above 1450.

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.