Unfortunately it is quite possible and since you've never been arrested, it appears that it has happened to you. This can be remedied, although not what I would call a "quick fix." I suggest you seek a consultation with an experienced criminal defense lawyer. Most of us provide free, no-obligation consultations. Where are you finding this information? www.galivanlaw.net
You mentioned that you have never been arrested in Illinois, but is it possible this arrest is from another state? If not, there is clearly an error which must be remedied ASAP. This can be a bit of a nightmare but can be accomplished with the help of an experienced criminal defense attoney. Speak to several lawyers and hire the one you like the best.
It is possible; but controlled substance charges are felonies and the fingerprint/booking procedure should have raised a flag. Do you have arrests in other states? You need to find out what county your conviction allegedly came from and consult a criminal defense attorney there. If someone did steal your identity; that person may be looking at new charges (other than the drug charge). You can't just walk in and have it go away. Those arrest/conviction records are shared amongst law enforcement databases and court orders will need to be signed by a judge clearing this up. If it was identity theft, you may be able to recoup your expenses for having this removed from your record from the person who stole your identity. (its not likely but it is theoretically possible) Having a felony conviction on your record is no joke with lots of collateral consequences you may not be aware of.