As your husband still lives in Illinois the Illinois courts have Subject Matter Jurisdiction, that is the right to hear the case. If your husband is the Petitioner then you will not have to appear if you have a signed Marital Settlement Agreement that handles all the issues in a divorce. Even though it is cordial I reccomend obtaining an attorney to do the paperwork properly because so many things can and do go wrong with people who represent themselves in Cordial Divorces.
There is no online divorce in Illinois.
yes you can. you can file here or in ga if you satisfy its residency requirements.
no, you cannot get a divorce on line. one of you has to make a court appearance. he can do.
Every state has their own laws as to residency requirements and the time you must reside in a state before they will entertain an action for divorce. Although I can not specifically state what Illinois law is, I can state that in all States, if one party fulfills the requirements, then the state will entertain the action. In your case you have the added point that you were married in the State. You should not have any problem doing a divorce in Illinois. That being said, I do not know if Illinois has any ability to file on line. I do know that New York State does not and I believe that Illinois does not either. You can usually get the documents you must file and filing instructions on line but you will probably have to file the paperwork and filing fees in the clerks office of the court. I think you would be better off finding an attorney in Illinois to assist you, in the long run, it will be faster and although it will cost it can save you money by making this go faster and avoid problems. Good Luck.