So basically you are letting an instructor use your barn and horses. No risk or maintenance expenses to them. All yours.
I would say you deserve at least 50% of whatever they charge for lessons. I might even try to go 60/40, since again, all the expenses are yours.
The going rate for ring rental (which is basically what your second question is) is between $10 and $25. Any of the places I have looked into it with have charged the fee on a per horse/rider basis. Not a time limit. One person can bring two horses, they pay twice.
Some places also offer a monthly fee. The place I know that does this the monthly fee is about 1/3 of what it costs to board there (this too is per horse/rider).