I think class 11th is most suitable for this condition as you don't want to mess up with the boards in class 12th so 11th is apt for this.
So, begin preparing for TOEFL and SAT together. SAT and TOEFL have a lot of similarities, except Speaking and listening in TOEFL and Maths in SAT.
3 months is more than enough time to prepare for both, in fact, if you already have elementary english perfected. TOEFL won't require more than a week. So don't worry for TOEFL.
SAT will take in reading skills that will demand your consistent concentration and focus. Maths in SAT is filthy easy! Just practice for 3 days straight and a 800 is guaranteed. Writing will also demand attention. So you need to work very hard to get 2000+. Afterall, You get scholarship on the basis of SAT. (there are other factors too).
Vocabulary will be a nagging topic (for me it was). And if you do it, you are half way through !
So, plan 3-months, when you work only for the SAT and the TOEFL. once cleared, get back to studies, work hard.