To answer the original question - why you have not received personal answers regarding the dismissal of your application, there are a multitude of possibilities. Foremost, professors may have simply decided to ignore the email. No one will be able to explain why this is the case, but it is certainly a possibility. It also seems that the correspondence with potential advisors was rather impersonal. From what you have suggested, the professors only said they would consider mentoring you if you where admitted. Responding in such a manner signifies a lack of personal investment on their part, and so I am not surprised it has been difficult getting a follow-up response.
Instead of emailing specific professors, you might try emailing the graduate or admissions coordinator at each of the schools you applied to. These individuals are typically more responsive than individual professors might be.
Looking towards next year, I think you have already identified the ways you can improve your application. The GRE and TOEFL scores must come up. Often applications whose standardized test scores fall below a threshold are tossed aside without consideration for the remainder of the application. At a minimum the goal is to not be in that category. Recommendation letters are tricky because of the time it takes to build a rapport with someone. The best bet is to keep working intensely with your current advisors and possibly branch out to a new lab. In general, a post-doc signing a letter of rec is not highly regarded. Instead you might want to have the post-doc write the letter because they know your more intimately, but have the PI of the lab sign the letter.
Good luck with admissions next cycle.