yes they are eligible for IIT and Aieee, As the IIT rules are modified last to last year. Now, you need to have atleast 60% in 10+2 or equivalent to appear in the JEE exam, the entrance test for IITs.
   Look, now a days , the pattern of IIT question paper is now as it was 10 to 20 years before. Now as the mains exam is not there so they cant ask you lengthy questions. Now they focus on the fundamentals rather than rote lerning and 2 -3 year constant learning of concepts. The questions which are asked in last  two years jee exam are relatively easy and mostly based in you 12th class knowledge. But the reasons behind the success of the coachings are the momentum which creates in your mind and soul around the year. Continues tests, quizes and the mentoring from the qualified faculty helps you to reach you goal more accurately and perfectly.
						

							
yes NRIs are eligible for IITs and aieee and infact there exists NRI quota in aieee.You have to fill in the form that you are NRI and take the normal exam procedure.


for iit a minimum of 60% in 12th board exams are needed which is exactly the same as the Indian nationals.
 
yes ofcourse you can clear iit-jee thru self study.But you have to be very very focused and organised and planned to sail thru this.Around three lakh students take iit-jee with full preparation and only first 8 thousand get thru it so you can see its not a cakewalk.You should definetly keep in touch with someone who have idea of this exam if you want to do it by your own at home.You can also take online help during the preparation.Every concept should be clear and questions practiced for better accuracy and speed in the exams.
askIITians offers multiple packages, catering to the needs of IIT JEE aspirants across the world.keep yourself uptodate with an online studycirle like we sort of develop at askIITians.