Your post is one long paragraph, digging through it to know precisely what your questions are is a bit tough. Try and make it easier on the reader by numbering your questions or using paragraphs if making a long post. I will try and address what I'm able to deduce as follows:
1. Yes, you may take advantage of the early filing memo and mail in your AOS package one or two months ahead of the current month. However, be aware of a slight possibility of the package getting rejected or denied. If the package gets rejected by the Chicago Lockbox, you simply re-file it. If it gets denied by your FO, you may or may not have enough time to get your FO to reconsider the denial.
2. Your F1 visa expiration date is immaterial. What matters is the duration of the status you were admitted. If your AOS package is officially received by USCIS prior to the expiration of your admitted status, you will still be considered to be in a legal status.
3. The AOS based EAD is not what gives you a legal status to stay in the US. It is the document that enables you undertake authorized employment. It's processing takes 3-4months, depending on your FO you may even end up getting the GC before the EAD card.
4. Your scholarship will most likely not be an acceptable means of proving you will not become a legal charge. I strongly recommend you get an I-134.
In conclusion, I also recommend you go through the AOS process document to enable you get a good understanding of what's involved. The link to the spreadsheet can be found on the first post on page one if this Thread.