must the renter report the resulting $6000 per year discount as income
to the IRS?
I would argue yes. You are essentially exchanging services for money - some chores in exchange for $500. Therefore, if we are dotting all our I's and crossing all our T's, the landlord should furnish you a 1099-Misc for your work.
If there is some question as to what the "normal" rent for the place
might be, what is the rule to determine it?
Generally, a landlord will take a look at what rental prices are around his/her property, then decide on what the rental price should be. The IRS states that:
A fair rental price for your property generally is the amount of rent
that a person who is not related to you would be willing to pay. The
rent you charge is not a fair rental price if it is substantially less
than the rents charged for other properties that are similar to your
property in your area.