Deadlines: Submitted vs. Completed

[Pricer]

I sent in one application on 1/7 and five more on 1/12. So far, only UVA, which I submitted on 1/12, has gone complete. I do not know why my other applications are still incomplete, except for USC, which required a dean's letter explaining university probation that I was unable to request until yesterday. Some of these applications have deadlines of 2/1. What happens if my files have not gone complete by then? Will I no longer be considered? Or as long as I have submitted all the proper documents through LSAC, does it just matter what day I submitted everything on?
Also, what about my situation at USC? My undergrad claims that it takes 7-10 days to process a request for a dean's letter. If that means 7-10 working days, it is possible that the dean's letter does not even get mailed until after 2/1. The only reason it took so long to get is because my undergrad was closed due to weather for nearly a week and they changed their policy on how to secure a dean's letter, but did not update their website nor were they even able to tell me the new policy over the phone. Only after an employee was emailing me information did she realize the mistake and tell me the new policy.
Every day that my file is incomplete is another day that the schools I wish to attend are filling spots. I know that there is nothing I can actually do about this, but I do not want my applications to get dismissed completely because I submitted them only 20 days before the deadline. It is very annoying to know I submitted my applications a week ago, one nearly two weeks ago, yet all of my status checkers say file incomplete.