Can I split my mortgage interest and property taxes between my gas royalty income and my personal deductions for my primary residence? Allocate the 2 expenses?

If the gas royalties stem from your primary or secondary residence, yes you can split them.   Use a reasonable allocation method, such as the percentage of income that stems from the royalties vs. your other income, or the percentage of square footage of the property that generates the royalty income vs. the total.