JEE

Hi Atharva, Both SAT and JEE are completely different so it will be best for you first focus on one test at a time, JEE is mainly high level quantitative and for engineering institutes in India. SAT, on the other hand, is for abroad studies and tests English and aptitude and basic high school maths. If you want to prepare for the tests together then schedule your routine differently. It's all about practice. Know your areas of weaknesses and practice. Basically, know what you want to study and if you want to study abroad. Once again, take one test at a time or you will end up spoiling both. For the books check these links:
https://magoosh.com/jee/best-books-jee-advanced/
https://blog.prepscholar.com/best-sat-prep-books.

Hi Shweta Sethi,
You are not late for SAT you can take it anytime during your 11th and 12th or even immediately after. There is no age limit or restriction, however the more you delay the more you will get late for the university application abroad. Preparation has to be as per your own routine and convenience. Both JEE and SAT are entirely different. SAT is mainly reasoning and aptitude with basic maths, JEE on the other hand is quantitative entirely. So you have to prioritize your requirement first, otherwise if you prepare for both simultaneously you may not do well in any of them. You have to decide if you want to go abroad now or later, if you can clear your JEE and get into IIT you can apply for your MS in USA or abroad. But if you are not confident of JEE then better go with SAT. Just make sure you don't waste valuable time.

Some of the popular entrance exams conducted for admissions into M.Arch programs other than NATA and JEE paper-2 are as follows:
1) GATE- Graduate Aptitude Test in Engineering is conducted jointly by Iits and the Indian Institute of Science. The minimum eligibility to take the test is graduation.
2) CEED- Common Entrance Examination for Design is conducted jointly by the Indian Institute of Science and Iits. The minimum eligibility to take the test is graduation in design, fine arts, or engineering from a recognised institution. The syllabus of the exam comprises questions related to design and general awareness, visual design, sketching, observation, design thinking ability, visual communication design etc. Interview is the last stage.
3) TANCET
Also, there are some colleges and universities that conduct their own entrance tests for admission to the course, while some offer direct admission too. Regards.