SAT

There is no restriction on who can take SAT. If you are planning to do Undergraduate degree in US, you should take SAT.
Another competitive exam for Undergraduate Admission in US is ACT.

Hi Juhi,
You can prepare for SAT and JEE together. Math asked in SAT is far easier than that in JEE.
But since there is no English related section in JEE, you will have to put in great efforts to prepare for SAT English/Verbal section.
Be aware that most students from India face troubles in SAT Verbal. Indian students perform pretty well in SAT math when compared to students from other countries (except China).

SAT is a competitive exam for undergraduate admission in US universities. Most universities in USA want that students should take this exam. There is another similar exam called ACT for US Universities.
Currently, SAT is out of 1600 marks.

Yes, you can go to US for undergraduate degree without SAT. There are many colleges in US which are SAT/ACT optional. This means that SAT or ACT is not a prerequisite to get admission in these colleges. One such college is Wheaton College in Norton Massachusetts, USA.

It is an excellent career option provided you can afford it.

Hi
Early decision starts in mid october /November and then January is the time so ensure that you have all results by then as different universities might have varying timeline.

Hi,
Since the test pattern has changed from May, you might not get much material free of cost. Try the following link for few papers or join some coaching to get more practice.
http://blog.prepscholar.com/printable-sat-practice-tests-4-free-official-tests

Dear Sakshi, know why SAT subjects tests are taken. 'Students typically choose which tests to take depending upon college entrance requirements for the schools to which they are planning to apply'. Therefore, you take the subjects which are related to your field of interest and to demonstrate your academic potential. Interestingly you did not mention which area of engineering. There is no minimum score for Stanford, students who are admitted are generally among the 80th or 90th percentile of test-takers. A score ranging above 720 would be safe.
Best Wishes

You can give SAT anytime, without worrying about eligibility. SAT exam does not have any specific eligibility criteria.

Dear Aarushi,
Yes, you can appear for SAT exams, irrespective of your stream. For more details, please check on the given link.
http://www.indiaeducation.net/international-exams/sat/sat-eligibility.aspx
All the very best.