What exactly do the terms of a "fixed 1/32 or 1/16 non-participating royalty interest" mean? Does all lease money go to the owner of the surface rights and the royalty owner will share only in oil, gas or mineral production?
Yes. If you will Google "Non-Participating Royalty Interests" you will get about 166K hits explaining what kind of interest it is.
Non-Participating means that you do not hold any executive rights, the rights to negotiate leases. You don't receive any Bonus or Rental Payments, only Royalties from the sales of produced oil and gas and related fluids.
There is a hybrid type of ownership, however, Non-Participating Mineral Interests. In that, you still do not have the right to negotiate any leases, but you do receive your share of any Bonus Payment and Rentals.
The attached articles and papers may help.41-NPRIvsNPMI.pdf (1.72 MB) 42-FRENCHvCHEVRONNPRINPMIfromBuddyCotten.pdf (75.9 KB) 43-MineralsvRoyalties.pdf (37.3 KB)