1. You should take 托福 ASAP. SJSU won't accept your application if you don't meet all the requirements. Or you can talk to the department to see if they are willing to conditionally accept you ,whcih mean you will need to still need to provide a 托福 score later.
2. What was your major in Junior college? If your major is not related to EE, then you will have to take all the requirement classes for EE major. If it's related, please bring your transcript and talk to department chair to check which classes can be waived.
3. You can try to apply for graduate program if you were major in EE in Junior College. There might be some classes you need to retake but it can save you some time. However, if you want to have a soild foundation, I would suggest you to get a BS first. And you get to learn a lot more than just EE.