THere are no such thing as "squatter's rights" in Illinois law or any law in the US. That is a term that is used in English common law and for some reason people believe it is applicable here in the US and it is not. The closest thing we have to "squatter's rights" in the US is a legal term called adverse possession -- and that occurs when one property owner tries to get a piece of the adjoining owner's property by putting up a fence or using it for a certain number of years -- and that property may then become theirs by operation of law.
You are in a situation where you have a month to month rental and a verbal agreement to pay that is enough to hold you to that in a court of law. The only way that you are permitted to withhold rent is if there are problems with the apartment that rise to the level of health, safety or sanitary violations -- you have no hot water or no heat or sewage is backing up into your apartment -- those are the types of violations that permit tenants to withhold rent. And, when you withhold rent, you then have to put it into an escrow account and if the landlord makes the repairs, the landlord is then entitled to be paid that rent money. If you withhold rent and then the LL evicts you, if the court does not find that the problems you are complaining enough are serious enough, the court will permit the eviction order AND order you to pay her all back rent monies -- which you can then be sued for and wages attached, etc if the LL wants to pursue it that far.
In your situation, you can take her to small claims court if you feel that you are paying too much in rent because the garage was not included or you feel that you are not getting what you should be getting as part of the deal -- and if you do not want to be evicted and owe the LL rent from a court order, the small claims court may be the best way for you to go with this.
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