I can't answer your specific questions because I don't practice in Illinois, however, if you picked the paper work up at the Courthouse or law library, there should be an instruction sheet available that explains the order in which to file the papers.
There might also be information available online through the county or State to help you process your pro se divorce. Also, there may be a free or low cost family law assistance center in your county.
Finally, you could try asking at the office where you will file the divorce paperwork. A clerk may be willing to tell you what order the papers are filed in.
you will need to file the petition for dissolution of marriage, and the other person would file an entry of appearance. The marital settlement agreement can not be filed until you appear before the judge, and testify that you agreed to it. You will note that you file your appearance pro se.