NFL rules are from
www.nfl.com/fans/rules/
Formation - NFHS:
The offense must have a minimum of seven men on the line of scrimmage. Anyone not on the line must clearly be a back (i.e. not breaking the plane of the nearest lineman's waist), except for a QB under center.
Formation - NFL:
Same, except that players not on the line must be one yard behind the line of scrimmage.
Eligibility - NFHS:
All backs are eligible, and linemen on either end of the line are eligible, but only if wearing a number 1-49 or 80-99.
Eligibility - NFL:
Backs are eligible, except for a QB under center. Ends are eligible unless a center, guard, or tackle. (I read this as meaning the snapper, and the two guys to either side of him.)
By "covered," we mean that an offensive lineman has another player outside of him also on the line. A "covered" player is ineligible, since he is not actually on the end. It sounds like the Bears may not have had six men on the line of scrimmage, but of course, I didn't see it, so...