At the university where I work, we recently went through a hiring process, which gave me some fresh inspiration for posts. What surprised me this time around was how many people thought they could go around the normal application process and get an exception.
Part of the application process was to write a short essay answering a few questions. There was a word limit, and when people ran up against it they were cut short. However, several candidates put their (much longer) essays into Microsoft Word and e-mailed them, saying that they didn't fit in the application.
If your essay doesn't fit the application, your essay is too long. Period.
Don't expect to be treated specially in an application process. The hiring manager is not your cheerleader. They're not going to say, "Well, 100 candidates filled out the online application, but this person sent us theirs via email so we'll have to print theirs out separately when we review them." They're going to say, "Well, this person can't follow directions, so we can eliminate them right now."
The same goes for deadlines. There may be a completely legitimate reason that you missed a deadline because of a million things going on in your life. But if a hiring manager has 100 applications waiting to be reviewed, they have zero motivation to grant a special exception for someone and add a 101st application to their pile.
It's legitimate to contact a company about their application if there is a genuine bug, defined as "Literally nothing you can do will allow you to access it / move forward to the next page." Even then, it is better to say, "I'm not sure what I'm doing wrong," than to go on the offensive and say, "Your application's broken," in case it turns out it was your error.
But you don't want to be the one contacting a company and saying, "Your application's broken because it won't let me upload my entire portfolio" (which they didn't ask for) or "I know it says to upload a PDF but I only have a Word document, and it won't let me upload it." Do not expect that anyone's going to go out of their way to accommodate you if you can't or don't want to follow directions.