If you are paying taxes, then the county is already assuming that you own a percentage of those tracts. There may be other owners also paying their percentage. So no, you cannot get more property without paying the other owners for it. Your ownership is tied to your deeds or probate documents.
Any offer to lease needs to state the royalty, bonus, and number of years. Those are the basic first step. Best to get a good oil and gas attorney to review any offer as the draft lease is usually not in the mineral owner’s favor and needs edits. I tend to go for a higher royalty if the area looks prospective.