Dont know about Il law, but in Ca, a party can demur to another party's answer, or can make a motion to strike. Parties can amend answers, cross claims, affirmative defenses, as long as the court grants leave to do so. As more info comes out in discovery, amendments may be appropriate.
In California, a party can amend their complaint once as a matter of course. The same goes for a Defendant's Answer and Affirmative Defenses. After that, leave of court is required. You will need to consult your Court's rules or a local attorney to determine if the same rules apply in your case.
The above is general legal analysis. It is not "legal advice" but analysis, and different lawyers may analyze this matter differently, especially if there are additional facts not reflected in the question. The above response does not create an attorney/client relationship. I am not your attorney until retained by a written retainer agreement signed by both of us. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here
As many and as often as the Judge allows. Also, you must motion for "leave to amend" a given pleading, and attach the amended version as an exhibit. In other words, you cannot simply file amended pleadings without prior permission to do so.
BTW, if the response raises "affirmative matter" and you fail to reply, you may be toast as it may be deemed admitted unless it is conclusory/argumentative/etc.
If, on the other hand, response merely admits/denies...it's a different matter.
This is not intended to be a comprehensive treatment of your questions. A lawyer with knowledge and smarts can use civil procedure in ways that will make your head spin...and possibly toss your case into quicksand or a state where you realize you lost your case before starting it on account of a 'legal technicality.'
But you know your opponent better than I so I can't really make any such sweeping assessment with the facts provided.
I wish you luck in the case. However, be sure to use caution in your litigation.
The author provides the preceding information as a service to the public. Author's response, as stated above, should not be considered legal advice. An initial attorney-client conference, based upon review of all relevant facts/documents, will be necessary to provide legal advice upon which the client should then rely.