1.This depends on schools where you apply. Yes, some of school (usually top private boarding schools have strict deadlines due to high application volume, especially from China) will not review application materials if scores are not submitted. It is called 'incomplete staus.' It is therefore very important for students to meet the deadlines with test score submission for applying to this type of school. There will be disadvantages for the late applications.
2Yes, you can decide on when you send your score. For more information, you must check SSAT's score reporting service.
3 This depends on student's preparedness and readiness. Receiving a good score from SSAT requires certain amount of time to prepare since English is not the first language for Chinese students. Also, the type of questions in SSAT, especially verbal sections, requires strong logical thinking skills . This means that Asian students need some time to get familiar with this types of questions. I would doubt that this skill will develop in one or two month of preparation.
4This also depends on schools. Some school would take the average scores from multiple test scores, some would take the best scores. However, I would suggest students to prepare enough before taking exams and perhaps taking more than three times would not be necessary.