Dessie,
1. The language you underline most likely refers to property tax or mortgage payments. Leases generally say that the company can pay your property taxes or mortgage payments to prevent foreclosure of your property, and generally you have to pay them back for that. This is standard language that you do not need to worry about.
2. Their first offer is probably not the best they can do. You should at least ask for more royalty and bonus and see what they might agree to. 15% is on the low end of the spectrum.
3. You should NOT hand over a signed lease until you have a check in hand. You should not accept their promise to pay you later, nor should you accept a "draft." You should let the company's landman know in advance that you will need to be paid by check before they get your lease.