Thanks for the excellent replies!
Instead of searching on firearm laws and gun laws, I searched hunting laws
and found following

From the Illinois Department of Natural Resources 2004-05 hunting guide.

"Hunting from Road.
It is unlawful to hunt, trap or discharge a
gun or bow and arrow device along, upon,
across or from a public roadway, highway or
right-of-way. Highway (right-of-way)
means the entire width between the boundary
lines of every public road. Roadway
means the portion of the public road that is
improved or ordinarily used for vehicle travel,
excluding the berm or shoulder."

AND

"Q. Is there a set distance from a roadway
I have to be in order to hunt?
A. No. There is no set distance. It is simply
unlawful to hunt, trap, or discharge a
gun or bow and arrow device along,
upon, across or from a public roadway,
highway, or right-of-way. (See page 8-9
of the digest for further explanation). The
only exception is that any person who
hunts on any property operated under a
Migratory Waterfowl Hunting Area Permit
where the principal use is to take wild
geese, cannot hunt geese from a pit or
blind that is within 200 yards of a public
right-of-way that is adjacent to any State
or Federal Waterfowl Refuge."

Also, the following applies to hunting but I'm not sure about target
practice. The neighbors "dwelling" is probably 100 yards, but less than 300
yards, from my property, meaning I could trap or hunt with a bow and arrow
or shotgun with shotshells.

"Hunting near Inhabited Dwellings
It is unlawful to hunt or allow a dog to
hunt within 300 yards of an inhabited
dwelling without first obtaining permission
of the owner or tenant of the dwelling.
EXCEPT: While trapping, hunting with bow
and arrow, or hunting with shotgun using
shotshells only, or on licensed game
breeding and hunting preserve areas, on
federally-owned and -managed lands, on
Department-owned, -managed, -leased or
-controlled lands and areas operated
under a Waterfowl Hunting Area permit, a
100-yard restriction shall apply."

Thanks again, the replies pointed me in the right direction!